TEMPUS AI, INC. AND as Trustee FIRST SUPPLEMENTAL INDENTURE Dated as of August 7, 2025

Exhibit 4.5

TEMPUS AI, INC.

AND

U.S. BANK TRUST COMPANY, NATIONAL ASSOCIATION

as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of August 7, 2025

0.75% Convertible Senior Notes due 2030

FIRST SUPPLEMENTAL INDENTURE, dated as of August 7, 2025 (this “Supplemental Indenture”), by and between Tempus AI, Inc., a Delaware corporation (the “Company”), as issuer, and U.S. Bank Trust Company, National Association, a national banking association organized under the laws of the United States of America, as trustee (the “Trustee”), to the Indenture, dated as of July 3, 2025 (as the same may be further supplemented or otherwise modified prior to the date hereof, the “Indenture”), between the Company and the Trustee.

WHEREAS, the Company has heretofore executed and delivered the Indenture, pursuant to which the Company issued its 0.75% Convertible Senior Notes due 2030 (the “Notes”) in the original aggregate principal amount of $750,000,000;

WHEREAS, at 11:59 p.m. Eastern Time on August 7, 2025, the Company shall convert from a corporation organized under the laws of the State of Delaware into a corporation organized under the laws of the State of Nevada (the “Nevada Corporation” and such transaction, the “Reincorporation”);

WHEREAS, pursuant to the Reincorporation, each share of Class A Common Stock (as defined in the Indenture) of the Company will convert into one share of Class A common stock, par value $0.0001 per share, of the Nevada Corporation (the “Nevada Corporation Common Stock”);

WHEREAS, the Reincorporation will constitute a Share Exchange Event pursuant to Section 14.07(a) of the Indenture;

WHEREAS, Section 14.07(a) of the Indenture provides, among other things, that in the event of a Share Exchange Event, the Company will execute with the Trustee a supplemental indenture providing that at and after the effective time of such Share Exchange Event, the right to convert each $1,000 principal amount of Notes shall be changed into a right to convert such principal amount of Notes into the kind and amount of shares of stock, other securities or other property or assets (including cash or any combination thereof) that a holder of a number of shares of Class A Common Stock equal to the Conversion Rate immediately prior to such Share Exchange Event would have owned or been entitled to receive (the “Reference Property”) upon such Share Exchange Event; provided, however, that at and after the effective time of the Share Exchange Event (A) the Company or the successor or acquiring Person, as the case may be, shall continue to have the right to determine the form of consideration to be paid or delivered, as the case may be, upon conversion of Notes in accordance with Section 14.02 of the Indenture and (B)(I) any amount payable in cash upon conversion of the Notes in accordance with Section 14.02 of the Indenture shall continue to be payable in cash, (II) any shares of Class A Common Stock that the Company would have been required to deliver upon conversion of the Notes in accordance with Section 14.02 of the Indenture shall instead be deliverable in the amount and type of Reference Property that a holder of that number of shares of Class A Common Stock would have received in such Share Exchange Event and (III) the Daily VWAP shall be calculated based on the value of a unit of Reference Property that a holder of one share of Class A Common Stock would have received in such Share Exchange Event;

WHEREAS, Section 10.01 of the Indenture provides that the Company and the Trustee may enter into any supplemental indenture without the consent of any Holder, among other things, (i) in connection with any Share Exchange Event, to provide that the Notes are convertible into Reference Property, subject to the provisions of Section 14.02 of the Indenture, and make such related changes to the terms of the Notes to the extent expressly required by Section 14.07 of the Indenture; or (ii) to make any change that does not adversely affect the rights of any Holder;

WHEREAS, in connection with the execution and delivery of this Supplemental Indenture, the Trustee has received an Officer’s Certificate and an Opinion of Counsel as contemplated by Sections 10.05 and 17.05 of the Indenture; and

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WHEREAS, the Company has requested that the Trustee execute and deliver this Supplemental Indenture and have satisfied all requirements necessary to make this Supplemental Indenture a valid instrument in accordance with its terms.

WITNESSETH:

NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company covenants and agrees with the Trustee as follows for the equal and ratable benefit of the Holders:

ARTICLE 1

DEFINITIONS

Section 1.01. Definitions in the Supplemental Indenture. Unless otherwise specified herein or the context otherwise requires:

(a) a term defined in the Indenture has the same meaning when used in this Supplemental Indenture unless the definition of such term is amended or supplemented pursuant to this Supplemental Indenture;

(b) the terms defined in this Article and in this Supplemental Indenture include the plural as well as the singular; and

(c) unless otherwise stated, a reference to a Section or Article is to a Section or Article of this Supplemental Indenture.

Section 1.02. Unit of Reference Property. “Unit of Reference Property” shall mean one share of Nevada Corporation Common Stock.

ARTICLE 2

EFFECT OF REINCORPORATION

Section 2.01.      Conversion of Notes. Pursuant to Section 14.07(a) of the Indenture, (a) at and after the effective time of the Reincorporation (the “Effective Time”), the right to convert each $1,000 principal amount of Notes into the Class A Common Stock shall be changed to a right to convert such principal amount of Notes into the number of Units of Reference Property equal to the Conversion Rate immediately prior to the Effective Time; (b)(i) the Company shall continue to have the right to determine the form of consideration to be paid or delivered, as the case may be, upon conversion of Notes in accordance with Section 14.02 of the Indenture and (c)(i) any amount payable in cash upon conversion of the Notes in accordance with Section 14.02 of the Indenture shall continue to be payable in cash, (ii) any shares of Class A Common Stock that the Company would have been required to deliver upon conversion of the Notes in accordance with Section 14.02 of the Indenture shall instead be deliverable in Units of Reference Property and (iii) the Daily VWAP shall be calculated based on the value of a Unit of Reference Property. The provisions of the Indenture, as modified herein, shall continue to apply, mutatis mutandis, to the Holders’ right to convert the Notes into the Reference Property.

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ARTICLE 3

MISCELLANEOUS

Section 3.01. Ratification of Indenture. The Indenture, as supplemented by this Supplemental Indenture, is in all respects ratified and confirmed, and this Supplemental Indenture shall be deemed part of the Indenture in the manner and to the extent herein and therein provided. Every holder of Notes heretofore or hereafter authenticated and delivered under the Indenture shall be bound thereby.

Section 3.02. Trustee Not Responsible for Recitals. The recitals herein contained are made by the Company and not by the Trustee, and the Trustee assumes no responsibility for the correctness thereof. The Trustee makes no representation as to the validity or sufficiency of this Supplemental Indenture. All of the provisions contained in the Indenture in respect of the rights, privileges, immunities, powers, and duties of the Trustee shall be applicable in respect of the Supplemental Indenture as fully and with like force and effect as though set forth in full herein.

Section 3.03. Successors. All agreements of the Company and the Trustee in this Supplemental Indenture will bind their respective successors.

Section 3.04. Governing Law. THIS SUPPLEMENTAL INDENTURE AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 3.05. Headings, Etc. The titles and headings of the articles and sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

Section 3.06. Execution in Counterparts. This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument. The exchange of copies of this Supplemental Indenture and of signature pages by facsimile or PDF transmission shall constitute effective execution and delivery of this Supplemental Indenture as to the parties hereto and may be used in lieu of the original Supplemental Indenture for all purposes. Signatures of the parties hereto transmitted by facsimile or PDF shall be deemed to be their original signatures for all purposes.

Section 3.07. Severability. In the event any provision of this Supplemental Indenture shall be invalid, illegal or unenforceable, then (to the extent permitted by law) the validity, legality or enforceability of the remaining provisions shall not in any way be affected or impaired.

Section 3.08. Waiver of Jury Trial. EACH OF THE COMPANY AND THE TRUSTEE HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS SUPPLEMENTAL INDENTURE OR THE TRANSACTIONS CONTEMPLATED HEREBY.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year first above written.

[Signature Page to First Supplemental Indenture]