Exhibit 5.1

1250 24th Street NW, Suite 700

Washington, DC 20037

202.349.8000

March 2, 2015

Board of Directors

Eagle Bancorp, Inc.

7830 Old Georgetown Road, Third Floor

Bethesda, Maryland 20814

RE: Eagle Bancorp, Inc. — Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Eagle Bancorp, Inc., a Maryland corporation (the “Company”) in connection with its registration statement on Form S-3 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) relating to the offer and sale from time to time, on a delayed or continuous basis pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act of 1933, as amended (the “Act”), of an indeterminate dollar amount of the following securities of the Company: (i) common stock, $0.01 par value per share (“Common Stock”); (ii) preferred stock, par value $0.01 per share, of one or more classes or series (“Preferred Stock”); (iii) depositary shares representing a fraction of a share of a particular class or series of Preferred Stock (“Depositary Shares”); (iv) warrants to purchase Common Stock, Preferred Stock or Depositary Shares (“Warrants”); (v) debt securities, which may be either senior debt or subordinated debt (“Debt Securities”); and (vi) Units consisting of any combination of the foregoing securities. The Common Stock, Preferred Stock, Depositary Shares, Debt Securities, Warrants and Units are collectively referred to as the “Securities.”

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, 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: (i) the amount and terms of Securities offered by the Company from time to time will have been specifically authorized for issuance by the Company’s Board of Directors or an authorized committee thereof, which such authorization will not have been modified or rescinded; (ii) any Securities issuable upon conversion, exchange, or exercise of any

Security being offered will have been duly authorized, created, and, if appropriate, reserved for issuance upon such conversion, exchange, or exercise; (iii) the Commission will have entered an appropriate order declaring effective the Registration Statement (including any required amendment thereto), and no order suspending its effectiveness will have been issued and remain in effect; (iv) all permits and governmental approvals required under federal or state law applicable to bank holding companies for any proposed issuance of Securities will have been obtained and remain in full force and effect; (v) a prospectus supplement will have been filed with the Commission describing the Securities offered thereby; (vi) the Company has or will have timely filed all necessary reports pursuant to the Securities Exchange Act of 1934, as amended, which are or will be incorporated by reference into the Registration Statement; (vii) all Securities will be issued and sold in compliance with applicable federal and state securities laws and solely in the manner stated in the Registration Statement and the applicable prospectus supplement; (viii) all Securities will be sold only against payment of the full amount of the consideration payable for such Securities, as set forth in the applicable prospectus supplement; (ix) no Securities will be sold in amounts in excess of the Company’s authorized and unreserved stock or other Security of the applicable class; (x) a definitive purchase, underwriting, warrant, deposit, unit or similar agreement with respect to the Securities will have been duly authorized and validly executed and delivered by the Company and the other parties thereto; (xi) the terms of the Securities will be established, the terms of all agreements entered into by the Company in connection with any issuance of Securities will be established, and all other actions by the Company in connection with any offer or sale of Securities will be effected, so as to not violate any applicable law or the Company’s charter or bylaws, or result in a default under or a breach of any agreement or instrument binding upon the Company and so as to comply with any requirements or restrictions imposed by any court, regulatory authority or other governmental body having jurisdiction over the Company. We have further assumed that each definitive purchase, underwriting, warrant, deposit, unit or similar agreement, and each indenture, and each amendment or supplement to any of the foregoing, will be governed by the laws of the State of Maryland.

To the extent that the obligations of the Company under Debt Securities may be dependent upon such matters, we assume for purposes of this opinion that: (i) each trustee is duly organized, validly existing and in good standing under the laws of its jurisdiction of organization; (ii) each trustee is duly qualified to engage in the activities contemplated by the indenture; (iii) an indenture has been duly authorized, executed and delivered by each trustee and constitutes the legally valid and binding obligation of such trustee, enforceable against the trustee in accordance with its terms; (iv) each trustee is in compliance, generally and with respect to acting as a trustee under the indenture, with all applicable laws and regulations; and (v) each trustee has the requisite organizational and legal power and authority to execute and deliver and to perform its obligations under the applicable indenture.

To the extent that the obligations of the Company under Warrants may be dependent upon such matters, we assume for purposes of this opinion letter that: (i) each warrant agent is duly organized, validly existing and in good standing under the laws of its jurisdiction of organization; (ii) each warrant agent is duly qualified to engage in the activities contemplated by the warrant agreement; (iii) each warrant agreement has been duly authorized, executed and

delivered by such warrant agent and constitutes the legally valid and binding obligation of such warrant agent, enforceable against such warrant agent in accordance with its terms; (iv) each warrant agent is in compliance, generally and with respect to acting as warrant agent under the warrant agreement, with all applicable laws and regulations; and (v) each warrant agent has the requisite organizational and legal power and authority to execute and deliver and to perform its obligations under the warrant agreement.

To the extent that the obligations of the Company under Depositary Shares may be dependent upon such matters, we assume for purposes of this opinion letter that: (i) each depositary is duly organized, validly existing and in good standing under the laws of its jurisdiction of organization; (ii) each depositary is duly qualified to engage in the activities contemplated by the deposit agreement; (iii) each deposit agreement has been duly authorized, executed and delivered by the depositary, and constitutes the legally valid and binding obligation of the depositary, enforceable against the depositary in accordance with its terms; (iv) each depositary is in compliance, generally and with respect to acting as depositary under the deposit agreement, with all applicable laws and regulations; and (v) each depositary has the requisite organizational and legal power and authority to execute and deliver and to perform its obligations under the deposit agreement.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations contained herein, we are of the opinion that:

1. When the Registration Statement has become effective under the Act, when the terms of the issuance and sale of the Common Stock have been duly established in conformity with the Company’s charter and when the Common Stock has been duly issued and sold as contemplated by the Registration Statement and the applicable prospectus supplement, the Common Stock will be validly issued, fully paid and non-assessable. The Common Stock covered in the opinion in this paragraph includes any Common Stock that may be issued upon exercise or otherwise pursuant to the terms of any Warrant.

2. When the Registration Statement has become effective under the Act, when the terms of the Preferred Stock and of its issuance and sale have been duly established in conformity with the Company’s charter, when appropriate articles supplementary to the Company’s charter with respect to the Preferred Stock have been duly filed with the Department of Assessments and Taxation of the State of Maryland (the “SDAT”), and when the Preferred Stock has been duly issued and sold as contemplated by the Registration Statement and the applicable prospectus supplement, the Preferred Stock will be validly issued, fully paid and non-assessable. The Preferred Stock covered in the opinion in this paragraph includes any Preferred Stock that may be issued upon exercise or otherwise pursuant to the terms of any Warrant, and any shares of any class or series of Preferred Stock underlying any Depositary Share.

3. When the Registration Statement has become effective under the Act, when the terms of the warrant agreement under which the Warrants are to be issued have been duly established and the warrant agreement have been duly executed and delivered, when the terms of such Warrants and of their issuance and sale have been duly established in conformity with the

applicable warrant agreement and when such Warrants have been duly executed and authenticated in accordance with the applicable warrant agreement and issued and sold as contemplated by the Registration Statement and the applicable prospectus supplement, such Warrants will constitute valid and legally binding obligations of the Company.

4. When the Registration Statement has become effective under the Act, the applicable indenture (including, for purposes of this paragraph, any supplemental indenture relating thereto setting forth the particular terms of the series of Debt Securities issued) has been established in conformity with the Company’s charter, duly executed and delivered by each party thereto and duly qualified under the Trust Indenture Act of 1939, as amended (the “Trust Indenture Act”); the Company has taken or caused to be taken all necessary corporate action to approve the issuance of and establish the terms of such Debt Securities, the terms of the offering thereof and related matters; the Debt Securities have been executed and authenticated in accordance with the terms of the indenture; and the Debt Securities have been issued and sold as contemplated by the Registration Statement and the applicable prospectus supplement, the Debt Securities to be issued under the applicable indenture will be valid and binding obligations of the Company.

5. When the Registration Statement has become effective under the Act, the related deposit agreement has been duly authorized and validly executed and delivered by the Company and by a bank or trust company appointed as depositary or depositary agent by the Company (the “Depositary”) that meets the requirements for a depositary as described in the Registration Statement or applicable prospectus supplement and/or as provided in the applicable deposit agreement; the Company has taken or caused to be taken all necessary corporate action to approve the issuance of and establish the terms of the Depositary Shares and related shares of Preferred Stock, the terms of the offering thereof and related matters, including the adoption of resolutions relating to the designations, preferences, limitations and relative rights of such related Preferred Stock when appropriate articles supplementary to the Company’s charter with respect to such related Preferred Stock shall have been duly filed with the SDAT; the shares of the related Preferred Stock have been deposited with the Depositary; and the depositary receipts representing the Depositary Shares have been executed and authenticated as contemplated by the Registration Statement and the applicable prospectus supplement, the Depositary Shares will be validly issued, fully paid and nonassessable.

6. When the Registration Statement has become effective under the Act, documents relating to the terms and conditions of the Units have been duly executed and delivered by the parties thereto; the Company has taken or caused to be taken all necessary corporate action to approve the issuance of and establish the terms of such Units and their component Securities, the terms of the offering thereof and related matters; the certificates evidencing the Units have been executed and authenticated in accordance with the terms of the relevant Unit document; and the Units and their component Securities have been issued and sold as contemplated by the Registration Statement and the applicable prospectus supplement, the Units will be valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The opinions expressed herein are further subject to: (i) the effect of bankruptcy, fraudulent transfer, insolvency, moratorium, reorganization, conservatorship, receivership, or other similar laws relating to or affecting the enforcement of the rights or remedies of creditors of FDIC-insured institutions or the enforcement of creditors’ rights or remedies generally; (ii) the effect of general principles of equity (whether applied in a court of law or in equity) which may limit the availability or enforceability of certain remedies; (iii) the possible unenforceability of indemnity and contribution provisions; (iv) the effect and possible unenforceability of choice of law provisions; (v) the possible unenforceability of provisions purporting to waive rights or defenses where such waiver is against public policy; (vi) the possible unenforceability of provisions purporting to exonerate any party for negligence or malfeasance, or to negate any remedy of any party for fraud; (vii) the possible unenforceability of forum selection clauses; (viii) the possible unenforceability of provisions permitting modification of an agreement only in writing; and (ix) the effect of laws requiring mitigation of damages.

Our examination of matters of law in connection with the opinions expressed herein has been limited to, and accordingly our opinions expressed herein are limited to, the federal securities laws, the laws of the State of Maryland, without reference to the conflicts of law or choice of law provisions thereof, and to the extent required in respect of the Debt Securities, the laws of the State of New York. We express no opinion with respect to the laws of any other jurisdiction. This opinion is given as of the date hereof, and we assume no obligation to advise you after the date hereof of facts or circumstances that come to our attention or changes in law that occur that could affect the opinions contained herein.

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 the reference to our Firm under the caption “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving such consent we do not thereby admit that we are in the category of persons the consent of which is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Commission thereunder.

	Sincerely


	/s/ BuckleySandler LLP