FORM OF SPONSOR INDEMNIFICATION AGREEMENT

Exhibit 10.5

Execution Version

FORM OF SPONSOR INDEMNIFICATION AGREEMENT

This Sponsor Indemnification Agreement (this “Agreement”) is dated as of [●], 2025, by and among Horizon Quantum Holdings Ltd., a Singapore public company limited by shares (“Holdco”), Horizon Quantum Computing Pte. Ltd., a Singapore private company limited by shares (the “Company”), and dMY Squared Sponsor, LLC, a Delaware limited liability company (the “Sponsor”). Capitalized terms used but not defined herein shall have the respective meanings ascribed to such terms in the Business Combination Agreement, dated as of September 9, 2025, entered into by and among dMY Squared Technology Group, Inc., a Massachusetts corporation (the “SPAC”), Holdco, Rose Acquisition Pte. Ltd., a Singapore private company limited by shares and wholly-owned subsidiary of Holdco, Horizon Merger Sub 2, Inc., a Massachusetts corporation and wholly-owned subsidiary of Holdco, and the Company (the “Business Combination Agreement”).

RECITALS

WHEREAS, on the date hereof, Holdco consummated the transactions contemplated by the Business Combination Agreement; and

WHEREAS, in connection with the Business Combination, the parties hereto desire to agree to certain matters as set forth herein.

AGREEMENT

NOW, THEREFORE, the parties hereto agree, as follows:

Holdco and the Company each hereby agrees to and shall indemnify, exonerate and hold harmless the Sponsor and its shareholders, members, directors, managers and officers (each, a “Sponsor Indemnified Person”), from and against any and all actions, causes of action, suits, claims, proceedings, investigations, liabilities, losses, damages, costs, fees, penalties, awards, settlements, judgments, decrees, amounts paid in settlement or expenses (including interest, assessments and other charges in connection therewith and reasonable fees and disbursements of attorneys and other professional advisors and costs of suit) (collectively, the “Sponsor Indemnified Liabilities”) arising out of or relating to any pending or threatened action, cause of action, suit, litigation, investigation, proceeding, inquiry, arbitration or claim against any of them or in which any of them may be a participant or may otherwise be involved (including as a witness) that arises out of or relates to the SPAC’s operations or conduct of its business (including, for the avoidance of doubt, the Transactions), and/or any claim against the Sponsor and/or a Sponsor Indemnified Person alleging any expressed or implied management, control or endorsement of any activities of the SPAC, or any express or implied association with Holdco, the Company, or the SPAC, or any of their respective affiliates (each of the foregoing, a “Claim”); provided, that the foregoing shall not apply to any Sponsor Indemnified Liabilities to the extent arising primarily out of (a) any breach by such Sponsor Indemnified Person of any other agreement between such Sponsor Indemnified Person, on the one hand, and the Company, Holdco or the SPAC or any of their respective Subsidiaries, on the other hand, or (b) the willful misconduct, gross negligence or bad faith of such Sponsor Indemnified Person.

Holdco and the Company will, at their expense, undertake the defense of any Claim with attorneys of their own choosing reasonably satisfactory in all respects to the applicable Sponsor Indemnified Person, subject to the right of such Sponsor Indemnified Person to undertake such defense as hereinafter provided. The applicable Sponsor Indemnified Person may participate in such defense with counsel of such Sponsor Indemnified Person’s choosing at the expense of Holdco and the Company. In the event that Holdco or the Company does not undertake the defense of any Claim within a reasonable time after the applicable Sponsor Indemnified Person has given the notice thereof, pursuant to Section 13 hereof, or in the event that such Sponsor Indemnified Person shall in good faith determine that the defense of any Claim by Holdco and/or the Company is inadequate or may conflict with the interest of such Sponsor Indemnified Person, such Sponsor Indemnified Person may, at the expense of Holdco and the Company and after giving notice, pursuant to Section 13 hereof, to Holdco or the Company of such action, undertake the defense of the Claim and compromise or settle the Claim, all for the account of and at the risk of Holdco and the Company.

Holdco and the Company shall pay all reasonable and documented costs and expenses (including, without limitation, attorneys’ fees and costs of experts) incurred by any Sponsor Indemnified Person in connection with such Sponsor Indemnified Person’s defense of any such Claim promptly after receipt of any statement therefor.

In the defense of any Claim against a Sponsor Indemnified Person, the Company and Holdco shall not, except with the prior written consent of such Sponsor Indemnified Person, consent to entry of any judgment or enter into any settlement that includes any injunctive or other non-monetary relief or any payment of money by such Sponsor Indemnified Person, or that does not include as an unconditional term thereof the giving by the person or persons asserting such Claim to such Sponsor Indemnified Person of an unconditional release from all liability on any of the matters that are the subject of such Claim and an acknowledgement that such Sponsor Indemnified Person denies all wrongdoing in connection with such matters.

The Company and Holdco shall not be obligated to indemnify a Sponsor Indemnified Person against amounts paid in settlement of a Claim if such settlement is effected by such Sponsor Indemnified Person without the prior written consent of the Company or Holdco, which shall not be unreasonably withheld or delayed.

If the indemnification provided for in this Agreement is for any reason not available to a Sponsor Indemnified Person as a matter of law in respect of any losses, claims, damages or liabilities referred to herein, then, in lieu of indemnifying such Sponsor Indemnified Person therefor, the Company and Holdco shall contribute to the amount paid or payable by such Sponsor Indemnified Person as a result of such losses, claims, damages or liabilities (and expenses relating thereto):

in such proportion as is appropriate to reflect the relative benefits to the Sponsor Indemnified Person, on the one hand, and the Company and Holdco, on the other hand, of the subject matter of this Agreement; or

if the allocation provided by clause (a) above is not available, in such proportion as is appropriate to reflect not only the relative benefits referred to in such clause (a) but also the relative fault of each of such Sponsor Indemnified Person and the Company and Holdco, as well as any other relevant equitable considerations.

The provisions of this Agreement are (x) intended to be for the benefit of, and will be enforceable by, each Sponsor Indemnified Person and each such Sponsor Indemnified Person’s heirs, legatees, representatives, successors and assigns, and shall be binding on all successors and assigns of Holdco and the Company and may not be terminated or amended in any manner adverse to such Sponsor Indemnified Person without its prior written consent and (y) in addition to, and not in substitution for, any other rights to indemnification or contribution that any such Sponsor Indemnified Person may have by contract or otherwise. For the avoidance of doubt, no amendment, alteration, or repeal of this Agreement or of any provision hereof shall limit or restrict any right of each Sponsor Indemnified Person under this Agreement in respect of any Claim (regardless of when such Claim is first threatened, commenced, or completed), issue, or matter therein arising out of, or related to, any action taken or omitted by such Sponsor Indemnified Person prior to such amendment, alteration, or repeal.

This Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby provided, that, for the avoidance of doubt, the foregoing shall not affect the rights and obligations of the parties under the Business Combination Agreement or any documents related thereto or referred to therein. This Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by the undersigned.

The Company and Holdco shall require and cause any of its successors (whether direct or indirect by purchase, merger, consolidation, or otherwise) to this Agreement, by written agreement in form and substance satisfactory to each Sponsor Indemnified Person, expressly to assume and agree to perform this Agreement to the fullest extent permitted by law. This Agreement shall be binding on the undersigned and each of its respective successors (whether direct or indirect by purchase, merger, consolidation, or otherwise), heirs and assigns and permitted transferees.

10.

The Law of the State of New York shall govern (a) all claims or matters related to or arising from this Agreement (including any tort or non-contractual claims) and (b) any questions concerning the construction, interpretation, validity and enforceability of this Agreement, and the performance of the obligations imposed by this Agreement, in each case without giving effect to any choice of law or conflict of law rules or provisions (whether of the State of New York or any other jurisdiction) that would cause the application of the Law of any jurisdiction other than the State of New York.

11.

Each party hereto submits to the exclusive jurisdiction of first, the New York Supreme Court, Commercial Division, located in the Borough of Manhattan in the City of New York, in the State of New York or if such court declines jurisdiction, then to any court of the State of New York or the Federal District Court for the Southern District of New York, in any Proceeding arising out of or relating to this Agreement, agrees that all claims in respect of the Proceeding shall be heard and determined in any such court and agrees not to bring any Proceeding arising out of or relating to this Agreement in any other courts. Nothing in this Section 11, however, shall affect the right of any party to serve legal process in any other manner permitted by Law or at equity. Each party hereto agrees that a final judgment in any Proceeding so brought shall be conclusive and may be enforced by suit on the judgment or in any other manner provided by Law or at equity. EACH PARTY HERETO HEREBY IRREVOCABLY WAIVES ALL RIGHTS TO TRIAL BY JURY IN ANY PROCEEDING BROUGHT TO RESOLVE ANY DISPUTE BETWEEN OR AMONG ANY OF THE PARTIES (WHETHER ARISING IN CONTRACT, TORT OR OTHERWISE) ARISING OUT OF, CONNECTED WITH, RELATED OR INCIDENTAL TO THIS AGREEMENT, THE TRANSACTIONS OR THE RELATIONSHIPS ESTABLISHED AMONG THE PARTIES UNDER THIS AGREEMENT. EACH PARTY FURTHER WARRANTS AND REPRESENTS THAT SUCH PARTY HAS REVIEWED THIS WAIVER WITH ITS LEGAL COUNSEL, AND THAT SUCH PARTY KNOWINGLY AND VOLUNTARILY WAIVES ITS JURY TRIAL RIGHTS FOLLOWING CONSULTATION WITH LEGAL COUNSEL.

12.

The parties hereto agree that irreparable damage would occur in the event any provision of this Agreement was not performed in accordance with the terms hereof and that the parties shall be entitled to specific performance of the terms hereof, in addition to any other remedy at law or in equity without the necessity of proving the inadequacy of money damages as a remedy and without bond or other security being required, this being in addition to any other remedy to which they are entitled at law or in equity. Each of the parties hereto hereby further acknowledges that the existence of any other remedy contemplated by this Agreement does not diminish the availability of specific performance of the obligations hereunder or any other injunctive relief. It is accordingly agreed that the parties hereto shall be entitled to seek an injunction or injunctions to prevent breaches of this Agreement and to enforce specifically the terms and provisions of this Agreement in the New York Supreme Court, Commercial Division, located in the Borough of Manhattan in the City of New York, in the State of New York, this being in addition to any other remedy to which such party is entitled at law or in equity. Each party hereto hereby further agrees that in the event of any action by any other party for specific performance or injunctive relief, it will not assert that a remedy at law or other remedy would be adequate or that specific performance or injunctive relief in respect of such breach or violation should not be available on the grounds that money damages are adequate or any other grounds.

13.

Any notice or other communication hereunder shall be sent in writing, addressed as specified below, and shall be deemed given: (a) if by hand or recognized courier service, by 5:00 PM on a Business Day, addressee’s day and time, on the date of delivery, and otherwise on the first Business Day after such delivery; (b) if by email, on the date of transmission; or (c) five (5) days after mailing by certified or registered mail, return receipt requested. Notices shall be addressed to the respective parties hereto as follows (excluding telephone numbers, which are for convenience only), or to such other address as a party hereto shall specify to the others in accordance with these notice provisions:

If to Holdco or the Company:

Horizon Quantum Computing Pte. Ltd.

29 Media Cir., #05-22

Singapore, 138565

Attention:

▇▇▇ ▇▇▇▇▇▇▇▇▇▇

E-mail:

with a copy (which shall not constitute notice) to:

▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇ & Schole LLP

▇▇▇▇ ▇▇▇▇▇▇ ▇▇ ▇▇▇ ▇▇▇▇▇▇▇▇, ▇▇▇▇ ▇▇

New York, NY 10105

	Attention:	▇▇▇▇ ▇. ▇▇▇▇▇▇; ▇▇▇▇▇ ▇. ▇▇▇▇▇▇
	Email:	▇▇▇▇▇▇▇@▇▇▇▇▇▇.▇▇▇; ▇▇▇▇▇▇▇@▇▇▇▇▇▇.▇▇▇

If to Sponsor:

dMY Squared Sponsor, LLC

▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇ ▇▇▇▇▇▇ ▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇

Las Vegas, Nevada 89144

Attention:

▇▇▇▇▇ ▇▇▇

Email:

with a copy (which shall not constitute notice) to:

White & Case LLP

▇▇▇▇ ▇▇▇▇▇▇ ▇▇ ▇▇▇ ▇▇▇▇▇▇▇▇

New York, NY 10020

	Attention:	▇▇▇▇ ▇▇▇▇▇▇▇▇▇▇; ▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇▇; ▇▇▇▇▇ ▇▇▇▇▇▇▇; ▇▇▇▇▇▇ ▇▇▇▇▇▇
	Email:	▇▇▇▇.▇▇▇▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇.▇▇▇; ▇▇▇▇▇▇▇▇.▇▇▇▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇.▇▇▇;

▇▇▇▇▇.▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇.▇▇▇; ▇▇▇▇▇▇.▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇.▇▇▇

[Signature Page Follows]

IN WITNESS WHEREOF, Holdco, the Company, and Sponsor have each caused this Sponsor Indemnification Agreement to be duly executed as of the date first written above.

	HORIZON QUANTUM HOLDINGS LTD.

	By:
	Name:
	Title:

	HORIZON QUANTUM COMPUTING PTE. LTD.

	By:
	Name:	▇▇▇ ▇▇▇▇▇▇▇▇▇▇
	Title:	Chief Executive Officer

	DMY SQUARED SPONSOR, LLC.

	By:
	Name:	▇▇▇▇▇ ▇. You
	Title:	Managing Member

[Signature Page to the Sponsor Indemnification Agreement]

FORM OF SPONSOR INDEMNIFICATION AGREEMENT

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