Not sure I understand the question. It seems like you're asking how a client would call it? If so, the fact that it's "'ASP.NET WebAPI using MVC 5" is irrelevant. It's "just" an HTTP call... what was used to implement things on the server side is not something that matters.
In .NET, HttpClient is the easiest way to make a REST call.
There's lots more that could be said on this topic... more than would fit in an article even. Do you have specific questions?