Exhibit 5.1

Seaport West 155 Seaport Boulevard Boston, MA 02210-2600   617 832 1000 main 617 832 7000 fax

April 23, 2024

Zapata Computing Holdings Inc.

100 Federal Street, Floor 20

Boston, MA 02110

Re: Registration Statement on Form S-1

Ladies and Gentlemen:

We are acting as counsel to Zapata Computing Holdings Inc., a Delaware corporation (the “Company”), in connection with its filing on the date hereof with the Securities and Exchange Commission (the “Commission”) of a registration statement on Form S-1 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of (i) the issuance by the Company of (x) up to 11,499,982 shares (the “Public Warrant Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), upon the exercise of up to 11,499,982 warrants to purchase shares of Common Stock (the “Public Warrants”) and (y) up to 13,550,000 shares (the “Private Warrant Shares” and, together with the Public Warrant Shares, the “Warrant Shares”) of Common Stock upon the exercise of up to 13,550,000 private placement warrants to purchase Common Stock (the “Private Placement Warrants” and, together with the Public Warrants, the “Warrants”) and (ii) the resale from time to time of (w) 15,850,336 outstanding shares (the “Outstanding Shares”, together with the Warrant Shares, the “Shares”)) of Common Stock, and (y) 13,550,000 Private Placement Warrants and (z) the Private Warrant Shares, in each case, by the selling securityholders named in the Registration Statement.

We have examined the Certificate of Incorporation and Bylaws of the Company, each as restated or amended to date, records of meetings and consents of the Board of Directors, or committees thereof, and records of the proceedings of stockholders deemed to be relevant to this opinion letter, each as provided to us by the Company, and the Registration Statement. We have also reviewed (i) the Business Combination Agreement by and among Andretti Acquisition Corp., Tigre Merger Sub, Inc., and Zapata Computing, Inc. dated as of September 6, 2023 and filed as Exhibit 2.1 to the Registration Statement, (ii) the Senior Secured Note Purchase Agreement between Zapata Computing, Inc. and certain noteholders a party thereto dated December 15, 2023 and filed as Exhibit 10.24 to the Registration Statement and related exchange agreements, (iii) the FPA Funding Amount PIPE Subscription Agreement among Andretti Acquisition Corp., Zapata Computing, Inc. and Sandia Investment Management LP, acting on behalf

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of certain funds dated as of March 25, 2024 and filed as Exhibit 10.29 to the Registration Statement, (iv) the Public Warrant Agreement between the Company and Continental Stock Transfer & Trust Company, as warrant agent (the “Public Warrant Agreement”), dated as of January 12, 2022 and filed as Exhibit 4.1 to the Registration Statement, pursuant to which the Public Warrants were issued, and (v) the Private Warrant Agreement between the Company and Continental Stock Transfer & Trust Company, as warrant agent (the “Private Warrant Agreement”, together with the Public Warrant Agreement, the “Warrant Agreements”), dated as of January 12, 2022 and filed as Exhibit 4.2 to the Registration Statement, pursuant to which the Private Warrants were issued. 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.

With regard to our opinion regarding the Warrant Shares, we have assumed that the applicable exercise price of each Warrant will not be adjusted to an amount below the par value per share of the Common Stock.

Our opinion expressed in numbered paragraph 3 below is qualified to the extent that (i) the enforceability or validity of any provision of any agreement, instrument or document or any rights granted thereunder may be subject to or affected by any bankruptcy, insolvency, reorganization, moratorium, preference, fraudulent conveyance, fraudulent transfer or similar law relating to or affecting the rights and remedies of creditors generally which may be in effect from time to time, (ii) the remedy of specific performance or any other equitable remedy may be unavailable in any jurisdiction or may be withheld as a matter of judicial discretion, (iii) equitable principles and principles of public policy may be applied in construing or enforcing any of the provisions of any agreement, instrument or document, (iv) the enforceability, validity or binding effect of any remedial provision of any agreement, instrument or document may be limited by applicable law, including, but not limited to, the application of principles of materiality, reasonableness, good faith and fair dealing, which may limit particular rights and remedies but not so as to interfere materially with the practical realization of the benefits intended to be provided by such agreement, instrument or document, and (v) rights to indemnification and contribution may be limited by federal and state securities laws or public policy. We express no opinion as to any provisions of the Private Placement Warrants that (a) provide for liquidated damages, default interest, late charges, monetary penalties, make-whole premiums or other economic remedies to the extent such provisions are deemed to constitute a penalty, (b) require the payment of attorneys’ fees, where such payment is contrary to law or public policy, (c) provide for advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary

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requirements, statutes of limitation, trial by jury or at law, or other procedural rights, (d) provide for exclusivity, election or cumulation of rights or remedies, (e) authorize or validate conclusive or discretionary determinations, or (f) provide for the severability, if invalid, of provisions to the foregoing effect. We express no opinion as to whether a state court outside the State of New York or a federal court of the United States would give effect to the choice of New York law or jurisdiction provided for in the Private Placement Warrants.

We have also assumed that (a) the Warrants and the Warrant Agreement have been duly authorized, executed and delivered by the parties thereto other than the Company, (b) the Warrants and the Warrant Agreement constitute and will constitute legally valid and binding obligations of the parties thereto other than the Company, enforceable against each of them in accordance with their respective terms and (c) the status of the Warrants and the Warrant Agreement as legally valid and binding obligations of the parties are not and will not be affected by any (i) breaches of, or defaults under, agreements, instruments or documents, (ii) violations of statutes, rules, regulations or court or government orders or (iii) failures to obtain required consents, approvals or authorizations from, or make required registrations, declarations or filings with, governmental authorities.

The opinion expressed below is limited to the General Corporation Law of the State of Delaware and, solely as to the Private Placement Warrants constituting legally binding obligations of the Company, the laws of the State of New York.

On the basis of the foregoing, it is our opinion that, as of the date hereof:

1. The Warrant Shares, when issued and paid for in accordance with the terms of the Warrants and the Warrant Agreements, will be validly issued, fully paid and non-assessable.

2. The Outstanding Shares have been validly issued and are fully paid and non-assessable.

3. The Private Placement Warrants constitute binding obligations of the Company.

This opinion is to be used only in connection with the offer and sale of the Shares and the Private Placement Warrants 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.

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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 your filing this opinion as an exhibit to the Registration Statement and to the reference to our firm in the prospectus constituting part of the Registration Statement under the heading “Legal Matters.” In giving such consent, we do not thereby admit that we are in 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.

Very truly yours,
FOLEY HOAG LLP
By:	/s/ Ryan M. Rourke Reed
	a Partner