Exhibit 5.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference in this registration statement on Form F-10 of Franco-Nevada Corporation of our report dated March 9, 2020 relating to the consolidated financial statements and effectiveness of internal control over financial reporting, which appears in the Exhibit 99.3 to Franco-Nevada Corporation’s Annual Report on Form 40-F for the year ended December 31, 2019. We also consent to the reference to us under the heading “Auditors, Transfer Agent and Registrar” in the short form base shelf prospectus which forms part of such registration statement.

/s/ PricewaterhouseCoopers LLP

Chartered Professional Accountants, Licensed Public Accountants

Toronto, Canada

April 28, 2020

PricewaterhouseCoopers LLP

PwC Tower, 18 York Street, Suite 2600, Toronto, Ontario, Canada M5J 0B2

T: +1 416 863 1133, F: +1 416 365 8215, www.pwc.com/ca