EX-5.1

We are familiar with the Registration Statement on Form S-1 (the “Registration Statement”) being filed by Zapata Computing Holdings Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on the date hereof. The Registration Statement relates to the offer and resale by Lincoln Park Capital Fund, LLC, an Illinois limited liability company (the “Investor”), of up to 13,000,000 shares of common stock, par value $0.0001 per share (“Common Stock”), of the Company, consisting of:

(a) 500,000 shares of Common Stock (the “Commitment Shares”) previously issued to the Investor under that certain purchase agreement, dated as of August 13, 2024, by and among the Company, Zapata Computing, Inc. and the Investor (the “2024 Purchase Agreement”) for its commitment to purchase shares of Common Stock thereunder; and

(b) up to 12,500,000 shares of Common Stock (the “Purchase Shares” and, together with the Commitment Shares, the “Shares”) that the Investor is committed to purchase from time to time under, and as set forth in, as applicable, (i) the 2024 Purchase Agreement or (ii) that certain purchase agreement, dated as of December 19, 2023, by and among the Company, Zapata Computing, Inc. and the Investor (the “2023 Purchase Agreement” and, together with the 2024 Purchase Agreement, the “Purchase Agreements”).

In arriving at the opinion expressed below, we have examined and relied upon the Certificate of Incorporation and Bylaws of the Company, each as amended and restated to date, the records of meetings and consents of the Company’s Board of Directors, or committees thereof, records of the proceedings of stockholders deemed to be relevant to this opinion letter, and the Purchase Agreements, each as provided to us by the Company, and the Registration Statement.

In addition, we have examined such matters of fact and questions of law as we have considered appropriate for the purposes of this letter. We have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as copies and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness of such documents.

Zapata Computing Holdings Inc.

September 3, 2024

Page 2

We have assumed that the purchase price or other consideration to be received by the Company for the Purchase Shares will be valid consideration equal to or in excess of the par value of the Common Stock. In rendering the opinion expressed below, we express no opinion other than as to the Delaware General Corporation Law.

On the basis of the foregoing, it is our opinion that (i) the Commitment Shares have been duly authorized and are validly issued, fully paid and non-assessable and (ii) the Purchase Shares have been duly authorized and, when issued and delivered by the Company to the Investor in accordance with the terms of the 2024 Purchase Agreement or the 2023 Purchase Agreement, as applicable, against the Company’s receipt of the purchase price or other consideration therefor, will be validly issued, fully paid and non-assessable.

This opinion is to be used only in connection with the offer and sale of the Shares while the Registration Statement is in effect.

This opinion is being delivered solely for the benefit of the Company and such other persons as are entitled to rely upon it pursuant to the applicable provisions of the Securities Act. This opinion may not be used, quoted, relied upon or referred to for any other purpose, nor may this opinion be used, quoted, relied upon or referred to by any other person, for any purpose, without our prior written consent.

This opinion is based upon currently existing statutes, rules and regulations and judicial decisions and is rendered as of the date hereof, and we disclaim any obligation to advise you of any change in any of the foregoing sources of law or subsequent developments in law or changes in facts or circumstances which might affect any matters or opinions set forth herein.

This opinion letter shall be interpreted in accordance with the Core Opinion Principles jointly issued by the Committee on Legal Opinions of the American Bar Association’s Business Law Section and the Working Group on Legal Opinions Foundation as published in 74 Business Lawyer 815 (2019).

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.