Exhibit 5.1

July 21, 2016

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 $150.0 million principal amount of its 5.00% Fixed to Floating Rate Subordinated Notes due August 1, 2026 (the “Notes”), pursuant the Subordinated Indenture (the “Base Indenture”), dated as August 5, 2014, between the Company and Wilmington Trust, National Association, as trustee (the “Trustee), as supplemented by the Second Supplemental Indenture, to be dated as of July 26, 2016, between the Company and the Trustee (the “Second Supplement” and collectively with the Base Indenture, the “Indenture”), and in accordance with the Underwriting Agreement dated July 21, 2016, by and among the Company and Sandler O’Neill & Partners, L.P., as representative of the several underwriters (the “Underwriting Agreement”).  The Notes will be offered and sold pursuant to a prospectus supplement dated July 21, 2016, including the accompanying prospectus dated March 2, 2015 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3, as amended (File No. 333-202405) (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 other 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 Second 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 and the Underwriting Agreement, 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, the possible unavailability of specific performance or injunctive relief and the possible unenforceability of provisions providing for indemnification and contribution.

Our opinion above, insofar as it pertains to the choice of law provisions of the instruments referred to in such opinion paragraphs in which New York law was chosen as the governing law, are rendered solely in reliance upon New York General Obligations Law Section 5-1401 and N.Y. CPLR 327(b), and are expressly conditioned upon the assumption that the legality, validity, binding effect and enforceability of said provisions will be determined by a court of the State of New York or a United States federal court sitting in New York and applying New York choice of law rules, including said Section 5-1401, or are rendered assuming that any court deciding any dispute involving such instruments will apply New York law by concluding that New York law bears a sufficient relationship to the relevant transaction to support the application of New York internal law consistent with due process. We express no opinion as to any constitutional limitations upon said Section 5-1401 or their effect, if any, upon any opinion herein expressed.

The opinions expressed herein are rendered as of the date hereof, are limited to the laws of the State of Maryland and the State of New York (excluding the securities laws thereof), 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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