Exhibit 5.1

Brownstein Hyatt Farber Schreck, LLP 702.382.2101 main 100 North City Parkway, Suite 1600 Las Vegas, Nevada 89106

August 27, 2025

Tempus AI, Inc.

600 West Chicago Avenue, Suite 510

Chicago, Illinois 60654

To the addressee set forth above:

We have acted as local Nevada counsel to Tempus AI, Inc., a Nevada corporation (the “Company”), in connection with the registration, for resale from time to time by the applicable selling stockholder(s) identified in the Prospectus Supplement (as defined below), of up to 1,268,033 shares (the “Shares”) of the Company’s Class A Common Stock, par value $0.0001 per share (the “Common Stock”), comprising (i) 1,124,714 shares of Common Stock issued by the Company pursuant to or in connection with that certain Agreement and Plan of Merger, dated as of August 22, 2025 (the “Merger Agreement”), by and among the Company, Giant Panda Merger Sub, Inc., a Delaware corporation, Paige.AI, Inc., a Delaware corporation (“Paige”), and Shareholder Representative Services LLC, a Colorado limited liability company, as securityholder representative, which includes 85,966 shares of Common Stock that may be released to certain to selling stockholders in connection with the release of the holdback pursuant to the terms of the Merger Agreement, (ii) 17,915 shares of Common Stock issued by the Company pursuant to that certain License Agreement, dated as of August 22, 2025 (the “License Agreement”), by and among the Company, Memorial Sloan-Kettering Cancer Center, a New York not-for-profit corporation (“MSK”), Memorial Hospital for Cancer and Allied Diseases, a New York not-for-profit corporation (“MH”), and Sloan-Kettering Institute for Cancer Research, a New York not-for-profit corporation (“SKI”), and (iii) 125,404 shares of Common Stock issued by the Company pursuant to that certain Settlement and Release Agreement, dated as of August 22, 2025 (together with the Merger Agreement and the License Agreement, the “Transaction Documents”), by and among the Company, Paige, MSK, MH and SKI, all as described in the Company’s Registration Statement on Form S-3 (File No. 333-289398), including the Prospectus, dated August 8, 2025, contained therein, as supplemented by the Prospectus Supplement, dated August 27, 2025 (the “Prospectus Supplement”, and collectively, the “Registration Statement”), as filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”). This opinion letter is being delivered at your request pursuant to the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In our capacity as such counsel, we are familiar with the proceedings taken and proposed to be taken by the Company in connection with the authorization, issuance and sale of the Shares as contemplated by, and as described in, the Transaction Documents and the Registration Statement. For purposes of this opinion letter, and except to the extent set forth in the opinion below, we have assumed that all such proceedings have been or will be timely completed in the manner presently proposed in the Transaction Documents and the Registration Statement.

www.bhfs.com

Tempus AI, Inc.

August 27, 2025

Page 2

For purposes of issuing the opinion hereinafter expressed, we have made such legal and factual examinations and inquiries, including an examination of originals or copies certified or otherwise identified to our satisfaction as being true copies of (i) the Registration Statement, (ii) the Company’s articles of incorporation and bylaws, each as amended to date, (iii) the Transaction Documents and (iv) such other agreements, instruments, corporate records and other documents as we have deemed necessary or appropriate. We have also obtained from officers, representatives and agents of the Company and from public officials, and have relied upon, such certificates, representations, assurances and public filings as we have deemed necessary and appropriate for the purpose of issuing this opinion letter.

Without limiting the generality of the foregoing, we have, with your permission, assumed without independent verification that (i) the statements of fact and all representations and warranties set forth in the documents we have reviewed are true and correct as to factual matters, in each case as of the date or dates of such documents and as of the date hereof; (ii) each natural person executing any of the documents we reviewed had at all relevant times and has sufficient legal capacity to do so; (iii) all documents submitted to us as originals are authentic, the signatures on all documents we reviewed are genuine, and all documents submitted to us as certified, conformed, photostatic, electronic or facsimile copies conform to the original document; (iv) the obligations of each party set forth in the Transaction Documents are its valid and binding obligations, enforceable in accordance with their respective terms; and (v) all corporate records made available to us by the Company, and all public records we have reviewed, are accurate and complete.

We are qualified to practice law in the State of Nevada. The opinion set forth herein is expressly limited to and based exclusively on the general corporate laws of the State of Nevada, and we do not purport to be experts on, or to express any opinion with respect to the applicability thereto or the effect thereon of, the laws of any other jurisdiction. We express no opinion concerning, and we assume no responsibility as to laws or judicial decisions related to, or any orders, consents or other authorizations or approvals as may be required by, any federal laws, rules or regulations, including, without limitation, any federal securities laws, rules or regulations, or any state securities or “blue sky” laws, rules or regulations.

Based on the foregoing, and in reliance thereon, and having regard to legal considerations and other information that we deem relevant, we are of the opinion that the Shares have been duly authorized and validly issued, and are fully paid and non-assessable.

The opinion expressed herein is based upon the applicable laws of the State of Nevada and the facts in existence on the date of this opinion letter. In delivering this opinion letter to you, we disclaim any obligation to update or supplement the opinion set forth herein or to apprise you of any changes in any laws or facts after such time as the Registration Statement is declared effective. No opinion is offered or implied as to any matter, and no inference may be drawn, beyond the strict scope of the specific issues expressly addressed by the opinion set forth herein.

Tempus AI, Inc.

August 27, 2025

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We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the reference to our firm in the Prospectus Supplement, under the heading “Legal Matters”. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Brownstein Hyatt Farber Schreck, LLP