Exhibit 5.1

Faegre Baker Daniels LLP

2200 Wells Fargo Center 90 South Seventh Street

Minneapolis Minnesota 55402-3901

Phone +1 612 766 7000

Fax +1 612 766 1600

September 9, 2016

CoLucid Pharmaceuticals, Inc.

222 Third Street

Cambridge, MA 02142

Ladies and Gentlemen:

We have acted as counsel to CoLucid Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a prospectus supplement dated September 9, 2016 (the “Prospectus Supplement”) to the prospectus dated June 24, 2016 (together, the “Prospectus”) relating to the offer and sale by the Company, pursuant to that certain Purchase Agreement dated September 9, 2016 (the “Purchase Agreement”), between the Company and Piper Jaffray & Co. and Barclays Capital Inc., as representatives of the several underwriters named in Schedule I thereto (the “Underwriters”), of 3,250,000 shares of the Company’s common stock, $0.001 par value per share, together with 487,500 shares for which the Underwriters have been granted an option to purchase (the “Shares”). The Prospectus forms a part of the Company’s registration statement on Form S-3 (No. 333-211865) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), which was declared effective by the Commission on June 24, 2016.

We have examined the Registration Statement, the Prospectus, the Purchase Agreement, the amended and restated bylaws of the Company and the amended and restated certificate of incorporation of the Company. We also have examined the originals, or duplicates or certified or conformed copies, of such corporate and other records, agreements, documents and other instruments and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth. As to questions of fact material to this opinion, we have relied upon certificates or comparable documents of public officials and of officers and representatives of the Company.

In rendering the opinions set forth below, we have assumed the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies and the authenticity of the originals of such latter documents.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Shares have been duly authorized and upon payment and delivery in accordance with the Purchase Agreement, the Shares will be validly issued, fully paid and nonassessable (i) if in the event issued as certificated shares, certificates representing such Shares have been duly executed by the President and Secretary of the Company, countersigned and registered by the Company’s transfer agent/registrar and delivered on behalf of the Company, or (ii) if in the event issued as uncertificated shares, upon authorization and registration thereof by action of the Company’s board of directors or a committee thereof.

We do not express any opinion herein concerning any law other than the Delaware General Corporation Law.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s current report on Form 8-K filed as of the date hereof and to the use of our name under the caption “Legal Matters” in the Prospectus Supplement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

This opinion is furnished to you in connection with the filing of the Prospectus Supplement, and is not to be used, circulated, quoted or otherwise relied upon for any other purpose. This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion speaks only as of the date hereof and we assume no obligation to revise or supplement this opinion thereafter.