Exhibit 5.1

Wyrick Robbins Yates & Ponton LLP

4101 Lake Boone Trail, Suite 300

Raleigh, North Carolina 27607

January 7, 2016

Board of Directors

Cempra, Inc.

6320 Quadrangle Drive, Suite 360,

Chapel Hill, NC 27517

Gentlemen:

We have acted as counsel to Cempra, Inc., a Delaware corporation (the “Company”), in connection with the proposed issuance of up to 4,791,667 shares of the Company’s common stock, $0.001 par value per share (the “Shares”) pursuant to the registration statement on Form S-3 (Registration Statement No. 333-203945), as filed by the Company with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Act”), as declared effective by the Commission on May 7, 2015, together with the exhibits thereto and the documents incorporated by reference therein (the “Registration Statement”), and the related base prospectus which forms a part of and is included in the Registration Statement (the “Base Prospectus”) and the related prospectus supplement for the Shares to be filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”).

The shares are to be sold pursuant to an Underwriting Agreement, dated as of January 6, 2016 (the “Underwriting Agreement”), by and among the Company and J.P. Morgan Securities LLC and Jefferies LLC as representatives of the several underwriters named therein, a copy of which has been filed as an exhibit to the Company’s Current Report on Form 8-K filed on January 7, 2016.

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Certificate of Incorporation, as amended to date, the Company’s Bylaws, as currently in effect, the Underwriting Agreement, and such instruments, documents, certificates and records that we have deemed relevant and necessary for the basis of our opinion hereinafter expressed. In such examination, we have assumed: (i) the authenticity of original documents and the genuineness of all signatures; (ii) the conformity to the originals of all documents submitted to us as copies; (iii) the truth, accuracy and completeness of the information, representations and warranties contained in the records, documents, instruments and certificates we have reviewed; and (iv) the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable.

This opinion is limited to the Delaware General Corporation Law, including the statutory provisions of the Delaware General Corporate Law and all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws.

We hereby consent to the use of our name wherever it appears in the Registration Statement and the Prospectus, and in any amendment or supplement thereto, the filing of this opinion as an exhibit to a current report on Form 8-K of the Company and the incorporation by reference of this opinion in the Registration Statement.

In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the Securities Act or the rules and regulations promulgated thereunder by the Commission.