Exhibit 5.1

250 Vesey Street • New York, New York 10281.1047

TELEPHONE: +1.212.326.3939 • FACSIMILE: +1.212.755.7306

November 12, 2025

Cassava Sciences, Inc.
6801 N. Capital of Texas Highway,
Building 1; Suite 300
Austin, Texas 78731

Re: Registration Statement on Form S-3 filed by Cassava Sciences, Inc.

Ladies and Gentlemen:

We have acted as counsel for Cassava Sciences, Inc., a Delaware corporation (“Cassava”), in connection with the authorization of the possible issuance and sale from time to time, on a delayed basis, by Cassava of up to $200,000,000 aggregate initial offering amount of: (i) shares of common stock, par value $0.001 per share, of Cassava (“Common Stock”); (ii) shares of preferred stock, par value $0.001 per share, of Cassava (“Preferred Stock”), in one or more series, certain of which may be convertible or exchangeable for Common Stock; (iii) depositary shares representing fractional interest in Preferred Stock of one or more series (“Depositary Shares”); (iv) warrants to purchase Common Stock, Preferred Stock, Debt Securities (as defined below) or a combination thereof (“Warrants”); (v) rights to purchase Common Stock, Preferred Stock, Debt Securities or other securities (“Rights”); (vi) senior debt securities of Cassava (“Senior Debt Securities”), in one or more series, certain of which may be convertible into or exchangeable for Common Stock or other securities; (vii) subordinated debt securities of Cassava (“Subordinated Debt Securities” and, collectively with the Senior Debt Securities, “Debt Securities”), in one or more series, certain of which may be convertible into or exchangeable for Common Stock or other securities; and  (viii) units consisting of one or more of the securities described in clauses (i) through (vii) above (the “Units”), in each case, as contemplated by Cassava’s Registration Statement on Form S-3 to which this opinion is an exhibit (as the same may be amended from time to time, the “Registration Statement”). The Common Stock, Preferred Stock, Depositary Shares, Warrants, Rights, Debt Securities and Units are collectively referred to herein as the “Securities.” The Securities may be offered and sold from time to time pursuant to Rule 415 under the Securities Act of 1933 (the “Securities Act”).

In connection with the opinions expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinions. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that:

AMSTERDAM • ATLANTA • BEIJING • BOSTON • BRISBANE • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS
DETROIT • DUBAI • DÜSSELDORF • FRANKFURT • HONG KONG • HOUSTON • IRVINE • LONDON • LOS ANGELES • MADRID
MELBOURNE • MEXICO CITY • MIAMI • MILAN • MINNEAPOLIS • MUNICH • NEW YORK • PARIS • PERTH • PITTSBURGH
SAN DIEGO • SAN FRANCISCO • SÃO PAULO • SHANGHAI • SILICON VALLEY • SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHINGTON

Cassava Sciences, Inc.

November 12, 2025

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Cassava Sciences, Inc.

November 12, 2025

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In rendering the foregoing opinions, we have assumed that: (i) the Registration Statement, and any amendments thereto, will have become effective (and will remain effective at the time of issuance of any Securities thereunder); (ii) a prospectus supplement describing each class or series of Securities offered pursuant to the Registration Statement, to the extent required by applicable law and relevant rules and regulations of the Securities and Exchange Commission (the “Commission”), will be timely filed with the Commission; (iii) the definitive terms of each class or series of Securities will have been established in accordance with the authorizing resolutions adopted by Cassava’s Board of Directors (or an authorized committee or subcommittee thereof), Cassava’s Restated Certificate of Incorporation, as amended (the “Certificate of Incorporation”), and applicable law; (iv) Cassava will issue and deliver the Securities in the manner contemplated by the Registration Statement and any Securities that consist of shares of capital stock will have been authorized and reserved for issuance, in each case within the limits of the then remaining authorized but unissued and unreserved amounts of such capital stock; (v) the resolutions authorizing Cassava to issue, offer and sell the Securities will have been adopted by Cassava’s Board of Directors (or an authorized committee or subcommittee thereof) and will be in full force and effect at all times at which the Securities are offered or sold by Cassava; (vi) all Securities will be issued in compliance with applicable federal and state securities laws; and (vii) any Deposit Agreement, Warrant Agreement, Subscription Rights Agreement, Indenture and Unit Agreement (each as defined below) will be governed by and construed in accordance with the laws of the State of New York and will constitute a valid and binding obligation of each party thereto other than Cassava.

With respect to any Securities consisting of Preferred Stock, we have further assumed that Cassava will issue and deliver the shares of Preferred Stock being issued and delivered after the filing with the Secretary of State of the State of Delaware of a certificate of amendment to the Certificate of Incorporation, approved by us, establishing the designations, preferences and rights of the class or series of Preferred Stock being issued and delivered.

With respect to any Securities consisting of Depositary Shares, we have further assumed that the Depositary Shares will be: (i) issued and delivered after authorization, execution and delivery of the deposit agreement, approved by us, relating to the Depositary Shares (the “Deposit Agreement”) to be entered into between Cassava and an entity selected by Cassava to act as depository (the “Depositary”); and (ii) issued after Cassava deposits with the Depositary shares of the Preferred Stock to be represented by such Depositary Shares that are authorized, validly issued, fully paid and nonassessable as contemplated by the Registration Statement and the Deposit Agreement.

With respect to any Securities consisting of Warrants, we have further assumed that: (i) the warrant agreement, approved by us, relating to the Warrants (the “Warrant Agreement”) to be entered into between Cassava and an entity selected by Cassava to act as the warrant agent (the “Warrant Agent”) will have been authorized, executed and delivered by Cassava and the Warrant Agent and (ii) the Warrants will be authorized, executed and delivered by Cassava and the Warrant Agent in accordance with the provisions of the Warrant Agreement.

Cassava Sciences, Inc.

November 12, 2025

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With respect to any Securities consisting of Rights, we have further assumed that: (i) the rights agreement, approved by us, relating to the Rights (the “Subscription Rights Agreement”) to be entered into between Cassava and an entity selected by Cassava to act as the purchase rights agent (the “Purchase Rights Agent”) will have been authorized, executed and delivered by Cassava and the Purchase Rights Agent and (ii) the Rights will be authorized, executed and delivered by Cassava and the Purchase Rights Agent in accordance with the provisions of the Subscription Rights Agreement.

With respect to any Securities consisting of any series of Debt Securities, we have further assumed that: (i) such Debt Securities will have been issued pursuant to an indenture that has been executed and delivered by Cassava and the applicable trustee in a form approved by us (the “Indenture”), and the Indenture will have been qualified under the Trust Indenture Act of 1939; (ii) all terms of such Debt Securities not provided for in the applicable Indenture will have been established in accordance with the provisions of the applicable Indenture and reflected in appropriate documentation approved by us and, if applicable, authorized, executed and delivered by Cassava and the applicable trustee; and (iii) such Debt Securities will be executed, authenticated, issued and delivered in accordance with the provisions of the applicable Indenture.

With respect to any Securities consisting of Units, we have further assumed that each component of such Unit will be authorized, validly issued, fully paid and nonassessable (to the extent applicable) and will constitute a valid and binding obligation of Cassava or any third party (to the extent applicable) as contemplated by the Registration Statement and the applicable unit agreement (the “Unit Agreement”), if any.

The opinions expressed herein are limited by bankruptcy, insolvency, reorganization, fraudulent transfer and fraudulent conveyance, voidable preference, moratorium or other similar laws and related regulations and judicial doctrines from time to time in effect relating to or affecting creditors’ rights generally, and by general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

Cassava Sciences, Inc.

November 12, 2025

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As to facts material to the opinions and assumptions expressed herein, we have relied upon oral or written statements and representations of officers and other representatives of Cassava and others. The opinions expressed herein are limited to the laws of the State of New York and the General Corporation Law of the State of Delaware, in each case as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of the Registration Statement. In giving such consent, we do not thereby admit that we are included 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.