Exhibit 99.5
Consent of Oppenheimer & Co. Inc.
Oppenheimer & Co. Inc. (“Oppenheimer”) hereby consents to the inclusion of our opinion letter, dated June 17, 2020, to the Board of Directors (in its capacity as such) of Rexahn Pharmaceuticals, Inc. (“Rexahn”)
included as Annex E, and to the references thereto under the captions “Prospectus Summary – Opinion of the Rexahn Financial Advisor,” “Prospectus Summary – Risk Factors,” “Risk Factors – Risks Related to the Merger – Ocuphire’s risk-adjusted
projections, which Oppenheimer relied on for its fairness opinion delivered to the Rexahn Board, assume that Ocuphire’s product candidates receive FDA approval. Ocuphire’s failure to obtain such FDA approval would adversely impact the combined
company’s potential to generate revenue, its business and its results of operations,” “Risk Factors – Risks Related to the Merger - The opinion received by the Rexahn Board from Oppenheimer is subject to a number of assumptions and it has not been,
and is not expected to be, updated to reflect changes in circumstances that may have occurred since the date of the opinion,” “The Merger – Background of the Merger”, “The Merger – Rexahn Reasons for the Merger,” “The Merger – Opinion of the Rexahn
Financial Advisor” and “The Merger – Ocuphire Financial Projections” in the proxy statement/prospectus/information statement relating to the proposed merger transaction involving Rexahn and Ocuphire Pharma, Inc, which proxy
statement/prospectus/information statement forms a part of this Registration Statement on Form S-4 of Rexahn (as amended, the “Registration Statement”).
In giving the foregoing consent, we do not admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended (the “Securities Act”), or the rules and
regulations promulgated thereunder, nor do we admit that we are experts with respect to any part of the Registration Statement within the meaning of the term “experts” as used in the Securities Act or the rules and regulations promulgated thereunder.
Notwithstanding the foregoing, it is understood that our consent is being delivered solely in connection with the filing of the above-mentioned Registration Statement and that our opinion is not to be used, circulated,
quoted or otherwise referred to for any other purpose, nor is it to be filed with, included in or referred to in whole or in part in any registration statement (including any subsequent amendments to the above-mentioned Registration Statement),
prospectus, proxy statement or any other document, without our prior written consent.
/s/ Oppenheimer & Co. Inc.
OPPENHEIMER & CO. INC.
Dated: September 30, 2020