Exhibit 5.1

March 4, 2015

Board of Directors

Eagle Bancorp, Inc.

7830 Old Georgetown Road, Third Floor

Bethesda, Maryland 20814

Gentlemen:

We have acted as counsel to Eagle Bancorp, Inc. (the “Company”) in connection with the offering of 2,449,479 shares of the Company’s common stock, $0.01 par value per share, in accordance with the Underwriting Agreement, dated as of March 4, 2015, between the Company and Sandler O’Neill + Partners, L.P. (the “Agreement”), pursuant to a prospectus supplement dated March 4, 2015, including the accompanying prospectus dated March 2, 2015 (such documents, collectively, the “Prospectus”), that forms part of the Company’s effective registration statement on Form S-3 (File No. 333-202405) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”).

In rendering this opinion, we have limited our examination to the legal and factual matters as we have deemed advisable, including examination of the Registration Statement, the Prospectus, as filed with the Commission pursuant to Rule 424(b) promulgated under the Securities Act, and such other corporate documents, records, information and certificates of the Company, certificates of public officials or government authorities and other documents as we have deemed necessary or appropriate as a basis for the opinions hereinafter expressed.  As to certain facts material to our opinions, we have relied upon statements, certificates or representations of officers and other representatives of the Company. We have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents and records submitted to us as originals, the conformity to original documents and records of all documents and records submitted to us as copies, and the truthfulness of all statements of fact contained therein. We have assumed the due authorization of such documents by all parties other than the Company and any subsidiary of the Company which is wholly owned (directly or indirectly) by the Company, the taking of all requisite action respecting such documents, the due execution and delivery of such documents by each other party, the legal capacity of all natural persons, and that all agreements are the valid and binding agreements of all parties to such agreements other than the Company and such wholly owned subsidiaries.

Based upon such examinations, and subject to the limitations, qualifications and assumptions stated herein, we are of the opinion that the Shares, when issued, delivered, and paid

for in the manner and in accordance with the terms set forth in the Registration Statement, the Prospectus and the Agreement, will be validly issued, fully paid, and non-assessable shares of the common stock of the Company.

The opinions expressed herein are rendered as of the date hereof, are limited to the laws of the State of Maryland, and we express no opinion on the laws of any other jurisdiction.

We hereby consent to the inclusion of this opinion as an exhibit to the Registration Statement on Form S-3, filed by the Company, and to the reference to our Firm contained in the Prospectus. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required by the Act or by the rules and regulations promulgated thereunder.

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