Only our Plesk Shared Hosting accounts support MVC4 and MCV5 applications. For more information, see What type of hosting account do I have?
When you publish your site using an MVC4 or MCV5 application, make sure you have .NET include the MVC dlls; they're included by default, so there's no action required on your end. You might also need to upload assemblies you want to use to a bin specific to your project.
For MVC5 applications using Entity Framework, you'll also need to change your CAS priv to "Full."