Exhibit 5.1

[Patton Boggs Letterhead]

July 23, 2013

Board of Directors

Rexahn Pharmaceuticals, Inc.

15245 Shady Grove Road, Suite 455

Rockville, MD 20850

(No. 333-175073)

Dear Ladies and Gentlemen:

We have acted as legal counsel to Rexahn Pharmaceuticals, Inc., a Delaware corporation (the “Company”) in connection with the offer and sale by the Company of an aggregate of 11,400,000 shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (“Common Stock”), and warrants (the “Warrants” and together with the Shares, the “Securities”) to purchase up to an aggregate of 3,990,000 shares of Common Stock (the “Warrant Shares”). We understand that the Securities are being offered and sold by the Company pursuant to a prospectus supplement, dated July 23, 2013 and the accompanying base prospectus, dated July 5, 2011, (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3 (File No. No. 333-175073) (the “Registration Statement”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In connection with the issuance of this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of: (i) the Registration Statement, including the Prospectus, and all exhibits thereto; (ii) a specimen stock certificate representing the Shares; (iii) the form of Warrant; (iv) the Amended and Restated Certificate of Incorporation of the Company, as presently in effect; (v) the Amended and Restated Bylaws of the Company, as presently in effect; and (vi) certain resolutions adopted by the Board of Directors of the Company (the “Board”) with respect to the issuance of the Securities. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates of public officials, certificates of officers or other representatives of the Company and others, and such other documents, certificates and records, as we have deemed necessary or appropriate as a basis for the opinion set forth herein. In addition, we have obtained from the officers of the Company certificates as to certain factual matters necessary for the purpose of this opinion and, insofar as this opinion is based on such matters of fact, we have relied solely on such certificates without independent investigation.

July 23, 2013

Page 2

In our examination, we have assumed and have not verified: (i) the legal capacity of all natural persons; (ii) the genuineness of all signatures (other than persons signing on behalf of the Company); (iii) the authenticity of all documents submitted to us as originals; (iv) the conformity with the originals of all documents supplied to us as copies; (v) the accuracy and completeness of all corporate records and documents made available to us by the Company; and (vi) that the foregoing documents, in the form submitted to us for our review, have not been altered or amended in any respect material to our opinion stated herein.

The opinions that we render herein are limited to those matters governed by the laws of the State of Delaware as of the date hereof. Our opinions expressed herein are as of the date hereof, and we assume no obligation to revise or supplement the opinions rendered herein should the above-referenced laws be changed by legislative or regulatory action, judicial decision or otherwise. We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof.

Based upon and subject to the foregoing, we are of the opinion that (i) the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and non-assessable, (ii) provided that the Warrants have been duly executed and delivered by the Company and duly delivered to the purchasers thereof against payment therefor; the Warrants, when issued and sold as contemplated in the Registration Statement and the Prospectus will be valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except as enforcement thereof may be limited by bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and by general principles of equity (including without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law), and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and non-assessable.

This opinion letter is provided for use solely in connection with the offer and sale of the Securities while the Registration Statement remains effective, and may not be used, circulated, quoted or otherwise relied upon for any other purpose without our express written consent. No opinion may be implied or inferred beyond the opinion expressly stated in the numbered paragraphs above.

July 23, 2013

Page 3

We hereby consent to your filing of this opinion with the Commission as an exhibit to a Current Report on Form 8-K to be incorporated by reference in the Registration Statement and to the use of our name under the caption “Legal Matters” in the Prospectus contained therein. In giving this consent, we do not admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission adopted under the Securities Act.