Exhibit 5.1

		Davis Polk & Wardwell LLP Paseo de la Castellana, 41 28046 Madrid davispolk.com

March 13, 2024

Banco Bilbao Vizcaya Argentaria, S.A.

Calle Azul, 4

28050 Madrid

Spain

Ladies and Gentlemen:

Banco Bilbao Vizcaya Argentaria, S.A., a sociedad anónima organized under the laws of the Kingdom of Spain (the “Company”), filed with the Securities and Exchange Commission a Registration Statement on Form F-3 (File No. 333-266391) (the “Registration Statement”), and the related Prospectus (the “Prospectus”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), certain securities, including $1,000,000,000 aggregate principal amount of the Company’s 5.381% senior preferred fixed rate notes due 2029 (the “2029 Notes”) and $1,000,000,000 aggregate principal amount of the Company’s senior non-preferred callable fixed-to-fixed rate notes due 2035 (the “2035 Notes” and each of the 2029 Notes and the 2035 Notes a “series of Securities” and together the “Securities”).

The 2029 Notes are to be issued pursuant to the provisions of the Senior Debt Securities Indenture dated as of July 28, 2016 (the “Senior Debt Securities Base Indenture”) between the Company and The Bank of New York Mellon, acting (except with respect to its role as security registrar) through its London Branch, as trustee, security registrar, transfer agent and paying agent, as amended and supplemented, with respect to the 2029 Notes, by the third supplemental indenture dated as of March 13, 2024 (the “2029 Notes Supplemental Indenture”). The 2035 Notes are to be issued pursuant to the provisions of the Senior Non-Preferred Debt Securities Indenture dated as of June 25, 2019 (the “Senior Non-Preferred Debt Securities Base Indenture,” and each of the Senior Debt Securities Base Indenture and the Senior Non-Preferred Debt Securities Base Indenture, a “Base Indenture”) between the Company and The Bank of New York Mellon, acting (except with respect to its role as security registrar) through its London Branch, as trustee, transfer agent, paying agent and security registrar, as amended and supplemented, with respect to the 2035 Notes, by the third supplemental indenture dated as of March 13, 2024 (the “2035 Notes Supplemental Indenture,” and each of the 2029 Notes Supplemental Indenture and the 2035 Notes Supplemental Indenture, a “Supplemental Indenture”), under which The Bank of New York Mellon, acting through its London Branch, has also agreed to act as calculation agent. Each Base Indenture, as so amended and supplemented by the applicable Supplemental Indenture with respect to the relevant series of Securities, is hereinafter referred to as an “Indenture.” The Securities are to be sold pursuant to the Underwriting Agreement (the “Underwriting Agreement”) incorporated by reference in the Pricing Agreement dated March 13, 2024 (together with the Underwriting Agreement, the “Pricing Agreement”) among the Company and the several underwriters named therein (the “Underwriters”).

We, as your special U.S. counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinions expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all documents filed with or submitted to the Securities and Exchange Commission through its Electronic Data Gathering, Analysis and Retrieval (“EDGAR”) system (except for required EDGAR formatting changes) conform to

		Banco Bilbao Vizcaya Argentaria, S.A.

the versions of such documents reviewed by us prior to such formatting (iv) all signatures on all documents that we reviewed are genuine, (v) all natural persons executing documents had and have the legal capacity to do so, (vi) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vii) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based upon the foregoing, and subject to the additional assumptions and qualifications set forth below, we advise you that, in our opinion, assuming that the Securities have been duly executed and authenticated in accordance with the provisions of the relevant Indenture and delivered to and paid for by the Underwriters pursuant to the Pricing Agreement, the Securities (other than the terms thereof expressed to be governed by Spanish law, as to which we express no opinion) will constitute valid and binding obligations of the Company, enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally, concepts of reasonableness and equitable principles of general applicability, and subject to possible judicial or regulatory actions giving effect to governmental actions or foreign laws affecting creditors’ rights, provided that we express no opinion as to the validity, legally binding effect or enforceability of any provision that permits holders to collect any portion of stated principal amount upon acceleration of the Securities to the extent determined to constitute unearned interest.

In connection with the opinion expressed above, we have assumed that the Company is validly existing as a corporation under the laws of the Kingdom of Spain. In addition, we have assumed that the Indentures and the Securities (collectively, the “Documents”) are valid, binding and enforceable agreements of each party thereto. We have also assumed that the execution, delivery and performance by each party to each Document to which it is a party (a) are within its corporate powers, (b) do not contravene, or constitute a default under, the bylaws or other constitutive documents of such party, (c) require no action by or in respect of, or filing with, any governmental body, agency or official and (d) do not contravene, or constitute a default under, any provision of applicable law, regulation or public policy or any judgment, injunction, order or decree or any agreement or other instrument binding upon such party.

We express no opinion as to (i) any provisions in the Indentures that purport to waive objections to venue, claims that a particular jurisdiction is an inconvenient forum or the like, (ii) whether a United States federal court would have subject-matter or personal jurisdiction over a controversy arising under the Indentures or the Securities or (iii) the effectiveness of any service of process made other than in accordance with applicable law.

We express no opinion as to (i) whether a New York State or United States federal court would render or enforce a judgment in a currency other than U.S. Dollars or enforce the exclusivity of the jurisdiction of the Spanish courts or waivers of holders and owners of Securities provided for in the Indentures and the Securities for the purposes described therein or (ii) the exchange rate that such a court would use in rendering a judgment in U.S. Dollars in respect of an obligation in any other currency. Further, we express no opinion as to the effect of fraudulent conveyance, fraudulent transfer or similar provisions of applicable law on the opinions expressed above.

We note that the choice-of-law provisions of the Indentures and the Securities, as applicable, are expressed to select Spanish law as the governing law for certain matters related to the Indentures and the Securities, including the authorization and execution of the Indentures, the authorization, issuance and execution of the Securities and certain provisions of the Indentures and the Securities related to the status and ranking of the Securities, the waiver of rights of set-off and the Spanish Bail-in Power (as such term is defined therein). We also note that the submission-to-jurisdiction provisions of the Indentures and the Securities, as applicable, are expressed to provide that the Spanish courts shall have exclusive jurisdiction in respect of any suit or proceeding arising out of or relating to the Securities or the Indentures arising out of, relating to or in connection with the exercise of the Spanish Bail-in Power by the Relevant Spanish Resolution Authority (as such terms are defined therein).

		Banco Bilbao Vizcaya Argentaria, S.A.

We also express no opinion with respect to Section 8.04 of the Senior Debt Securities Base Indenture (as amended by Section 2.01(z) of the 2029 Notes Supplemental Indenture), Section 8.04 of the Senior Non-Preferred Debt Securities Base Indenture (as amended by Section 2.01(m) of the 2035 Notes Supplemental Indenture), the Section entitled “Substitution and Modification” of each series of Securities or any provision of the Indentures or the Securities relating to the Spanish Bail-in Power (as such term is defined therein).

We are members of the Bar of the State of New York and the foregoing opinion is limited to the laws of the State of New York and the federal laws of the United States of America, except that we express no opinion as to any law, rule or regulation that is applicable to the Company or the Documents or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to any party to any of the Documents or any of its affiliates due to the specific assets or business of such party or such affiliate. Insofar as the foregoing opinion involves matters governed by the laws of the Kingdom of Spain, we have relied, without independent inquiry or investigation, on the opinion of J&A Garrigues, S.L.P., Spanish legal counsel for the Company, dated as of March 13, 2024, to be filed as an exhibit to a report on Form 6-K to be filed by the Company on the date hereof, and our opinion is subject to the qualifications, assumptions and limitations set forth therein.

We hereby consent to the filing of this opinion as an exhibit to a report on Form 6-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Validity of the Securities” in the prospectus supplement which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP