Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

June 24, 2021                            

New York Community Bancorp, Inc.,

615 Merrick Avenue,

Westbury, NY 11590.

Ladies and Gentlemen:

In connection with the registration under the Securities Act of 1933 (the “Act”) of 216,123,141 shares (the “Securities”) of common stock, par value $0.01 per share, of New York Community Bancorp, Inc., a Delaware corporation (the “Company”), we, as your counsel, have examined such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion.

Upon the basis of such examination, we advise you that, in our opinion, when the registration statement relating to the Securities has become effective under the Act, and the Securities have been duly issued and delivered as provided in the Agreement and Plan of Merger, dated as of April 24, 2021, by and among the Company, 615 Corp., a Delaware corporation, and Flagstar Bancorp, Inc., a Michigan corporation (the “Merger Agreement”), as contemplated by the Registration Statement, the Securities will be validly issued, fully paid and nonassessable.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in any registration statement or any related prospectus or other offering material relating to the offer and sale of the Securities.

The foregoing opinion is limited to the Federal laws of the United States and the General Corporation Law of the State of Delaware, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

We have relied as to certain matters upon information obtained from public officials, officers of the Company and other sources believed by us to be responsible and we have assumed that the signatures on all documents examined by us are genuine, an assumption which we have not independently verified.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us under the heading “Legal Matters” in the joint proxy statement/prospectus contained therein. 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 Act.

Very truly yours,

/s/ Sullivan & Cromwell LLP