Only our Plesk Windows Shared Hosting accounts support MVC4 and MCV5 applications.
When you publish your site via Visual Studio using an MVC4 or MCV5 application, make sure you have .NET include the MVC dlls; they're included by default usually. 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." - Our servers do support Full Trust aswell by default.