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Exhibit 5.1

November 21, 2022

Cassava Sciences, Inc.

N. Capital of Texas Highway, Building 1; Suite 300

Austin,  TX78731

Re:1,666,667 Shares of Common Stock of Cassava Sciences, Inc.

Ladies and Gentlemen:

We have acted as counsel toCassava Sciences, Inc., a Delaware corporation (the “Company”), in connection with the offer and saleby the Company of 1,666,667 shares of the Company’s common stock, par value $0.001 (the “Shares”), pursuant to the Company’sregistration statement on Form S-3(Registration Statement No. 333-252931)  (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), which became effective immediately upon its filing on February 10, 2021,  the prospectus dated February 10,2021, included therein (the “Base Prospectus”), and the prospectus supplement dated November 18, 2022, filed with the Commission pursuant to Rule 424(b) of the rules and regulations of the Act(the “Prospectus Supplement”). The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.” The Shares are to be sold by the Company in the manner described in the Registration Statement and the Prospectus. The Company is filing this opinion letter with the Commission on a Current Report on Form 8-K (the “Current Report”).

In connection with rendering the opinion set forth below, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of (i) the Amended and Restated Certificate of Incorporation of the Company, as amended and restated through the date hereof, (ii) the Amended and Restated Bylaws of the Company, as amended and restated through the date hereof, (iii) certain resolutions of the Board of Directors of the Company and certain resolutions of the Finance Committee thereof relating to the issuance, sale and registration of the Shares, (iv) the Registration Statement, (v) the Prospectus and (vi)  such corporate records of the Company, certificates of public officials, officers of the Company and other persons, and such other documents, agreements and instruments as we have deemed relevant and necessary or appropriate as a basis for the opinion set forth below.

In our examination, we have assumed the legal capacity of allnatural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, and the authenticity of the originals of such

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copies. In making our examination of documents executed or to be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents and the validity and binding effect thereof on such parties. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

Our opinion herein is limited to the General Corporation Law of the State of Delaware.

Based upon and subject to the foregoing, we are of the opinion that the Shares have been duly authorized by the Company and, when such Shares are issued and paid for as described in the Registration Statement and the Prospectus, will be validly issued, fully paid and non-assessable.

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

Very truly yours,

/s/ ORRICK, HERRINGTON & SUTCLIFFE LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP

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