Exhibit 5.1

July 31, 2014

Board of Directors

Eagle Bancorp, Inc.

7830 Old Georgetown Road, Third Floor

Bethesda, Maryland 20814

RE:                                     Eagle Bancorp, Inc. — Subordinated Debt

Gentlemen:

We have acted as counsel to Eagle Bancorp, Inc. (the “Company”) in connection with the offer and sale by the Company of an aggregate of $70 million principal amount of its 5.75% Subordinated Notes due September 1, 2024 (the “Notes”), pursuant the Subordinated Indenture (the “Base Indenture”), to be dated as August 5, 2014, between the Company and Wilmington Trust, National Association, as trustee (the “Trustee), as supplemented by the First Supplemental Indenture, to be dated as of August 5, 2014, between the Company and the Trustee (the “First Supplement” and collectively with the Base Indenture, the “Indenture”), and in accordance with the Underwriting Agreement dated July 31, 2014, by and among the Company, EagleBank, and you (the “Underwriting Agreement”).  The Notes will be offered and sold pursuant to a prospectus supplement dated July 31, 2014, including the accompanying prospectus dated October 5, 2012 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3, as amended (File No. 333-183054) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”).

In rendering this opinion, we have limited our investigations to the legal and 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, the Indenture 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 that the Base Indenture and First Supplement are executed in the form reviewed, without material revision.

Based upon such examinations, and subject to the limitations, qualifications and assumptions stated herein, we are of the opinion that the Notes have been duly authorized, and assuming their due authentication by the Trustee, when they have been duly executed, issued and delivered in accordance with the terms of the Indenture, will constitute valid and legally binding obligations of the Company entitled to the benefits of the Indenture.

Our opinion is subject to bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, fraudulent transfer and other similar laws relating to or affecting creditors’ rights generally and to general equitable principles (regardless of whether considered in a proceeding in equity or at law), including concepts of commercial reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief.

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 and to the reference to our Firm contained therein. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or by the rules and regulations promulgated thereunder.

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