Exhibit 5.1

79 Wellington St. W., 30th Floor
Box 270, TD South Tower
Toronto, Ontario  M5K 1N2 Canada
P. 416.865.0040 | F. 416.865.7380 www.torys.com

June 15, 2018

Franco-Nevada Corporation
Commerce Court
199 Bay Street, Suite 2000
Toronto, Ontario, Canada
M5L 1G9

Dear Sirs/Mesdames:

Re: Franco-Nevada Corporation (the “Company”) — Dividend Reinvestment Plan

We have acted as counsel for the Company, a corporation formed under the federal laws of Canada, in connection with the filing of a registration statement on Form F-3 (the “Registration Statement”) with the Securities and Exchange Commission (“SEC”) pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder, in respect of 2,500,000 common shares of the Company (the “Common Shares”) issuable pursuant to the Company’s Dividend Reinvestment Plan (the “Plan”). This opinion is being furnished to you as a supporting document for such Registration Statement.

We have reviewed the Plan and the Registration Statement and made such investigations and examined originals or copies, certified or otherwise identified to our satisfaction, of such certificates of public officials and of such other certificates, documents and records as we have considered necessary or relevant for the purposes of the opinions hereinafter expressed. In such examinations we have assumed:

1.the legal capacity of all individuals, the genuineness of all signatures, the authenticity and completeness of all documents submitted to us as originals and the completeness and conformity to authentic originals of all documents submitted to us as certified, photostatic, conformed, notarial or facsimile copies;

2.all facts set forth in the official public records, certificates and documents supplied by public officials and the Company, or otherwise conveyed to us by public official or the Company are complete, true and accurate as of the date of this opinion letter; and

3.the accuracy, currency and completeness of the indices and filing systems maintained by the public offices and registries where we have searched or enquired or have caused searches or enquiries to be made and of the information and advice provided to us by appropriate government, regulatory or other like officials with respect to those matters referred to herein.

The opinion expressed below is limited to the laws of the Province of Ontario, including the federal laws of Canada applicable therein on the date hereof and we express no opinion herein with respect to the laws of any other jurisdiction or as to matters governed by the laws of any other jurisdiction. The statutory provisions, regulations, and interpretations upon which our opinion is based are subject to change, and such changes could apply retroactively. We assume no responsibility to advise you of any subsequent changes in existing law or facts, nor do we assume any responsibility to update this opinion with respect to any matters expressly set forth herein, and no opinions are to be implied or may be inferred beyond the matters expressly so stated.

Based on the foregoing, we are of the opinion that the Common Shares to be issued pursuant to the Plan have been duly authorized and, when and to the extent issued in accordance with the Plan, such Common Shares will be outstanding as validly issued, fully paid and non-assessable shares.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement, or any amendment pursuant to Rule 462 under the Act, and to the reference to us under the heading “Legal Matters” in the Prospectus included in the Registration Statement, or any amendment pursuant to Rule 462 under the Act. In giving this consent, we do not hereby agree that we come within the category of persons whose consent is required by the Act.

Yours very truly,

/s/ Torys LLP

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