ASP.NET MVC 5 uses Identity framework for
authorization and authentication processes. You need to look for a method in Identity framework, not in MVC 5; which is just the version of MVC framework.
This article[
^] on ASP.NET's official documentation, explains the code that you can use to change password, or perform other stuff with user's account. You will find answers to other questions there also. Just navigate through the menu and links. It guides you to reset password, also to change the password. For other detailed information on
UserManager.ChangePassword
function of Identity framework of ASP.NET, please read
MSDN resource[
^].