Exhibit 5.1

Mark B. Weeks

T: +1 650 843 5011

mweeks@cooley.com

April 19, 2023

Vaxcyte, Inc.

825 Industrial Road

Suite 300

San Carlos, California 94070

Ladies and Gentlemen:

You have requested our opinion, as counsel to Vaxcyte Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of up to 13,030,000 shares (the “Shares”) of its common stock, par value $0.001 per share (including up to 1,830,000 Shares that may be sold pursuant to the exercise of an option to purchase additional Shares), and pre-funded warrants (the “Warrants”) to purchase up to 1,000,000 shares of common stock of the Company (the “Warrant Shares”), pursuant to a Registration Statement on Form S-3 (Registration Statement No. 333-257622) (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), the prospectus included in the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated April 18, 2023, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Securities Act (together with the Base Prospectus, the “Prospectus”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and Prospectus, (b) the form of Warrant to be filed as an exhibit to a Current Report on Form 8-K, (c) the Company’s certificate of incorporation and bylaws, as currently in effect, and (d) originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials 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 thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

With regard to our opinion regarding the Warrants and the Warrant Shares, we express no opinion to the extent that future issuances of securities of the Company, anti-dilution adjustments of outstanding securities of the Company, and or other matters cause the Warrants to be exercisable for more shares of the Company’s common stock than the number available for issuance by the Company. Further, we have assumed the exercise price of the Warrants will not be adjusted to an amount below the par value per share of the Common Stock.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware and, as to the Warrants constituting valid and legally binding obligations of the Company, the laws of the State of New York. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

t: +1 650 843 5000 f: +1 650 849 7400 cooley.com

Vaxcyte, Inc.

April 19, 2023

Page Two

With regard to our opinion concerning the Warrants constituting valid and binding obligations of the Company:

(i) Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law;

(ii) Our opinion is subject to the qualification that (a) the enforceability of provisions for indemnification or limitations on liability may be limited by applicable law and by public policy considerations, and (b) the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought;

(iii) We express no opinion with respect to any provision of the Warrants that: (a) relates to the subject matter jurisdiction of any federal court of the United States of America or any federal appellate court to adjudicate any controversy related to the Warrants; (b) specifies provisions may be waived in writing, to the extent that an oral agreement or implied agreement by trade practice or course of conduct has been created that modifies such provision; (c) contains a waiver of an inconvenient forum; (d) provides for liquidated damages, default interest, late charges, monetary penalties, prepayment or make-whole payments or other economic remedies; (e) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, service of process or procedural rights; (f) restricts non-written modifications and waivers; (g) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy; (h) relates to exclusivity, election or accumulation of rights or remedies; or (i) provides that provisions of the Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable; and

(iv) We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law provided for in the Warrants.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares, when sold and issued against payment therefor in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid, and nonassessable, (ii) the Warrants, when duly delivered against payment therefor in accordance with the Registration Statement and the Prospectus, will be valid and legally binding obligations of the Company, and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement. 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 and the rules and regulations of the Commission promulgated thereunder.

Vaxcyte, Inc.

April 19, 2023

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Sincerely,
Cooley LLP
By:	/s/ Mark B. Weeks
	Mark B. Weeks