I would start of with reading the requirements in which the following is a problem I see right away:
- ASP.NET 4.5 (MVC 5.0)
- Microsoft .NET Framework 4.5.1 or above
Than I am not sure about using nop-commerce as a way to get a shopping card into your project. At least that is what I understand from your message.
I think you want to create your own shoppingcard. See following links:
online example and tutorial: http://www.asp.net/mvc/tutorials/mvc-music-store
offline tutorial (PDF): http://docrepository.googlecode.com/files/MVC%20Music%20Store%20-%20Tutorial%20-%20v1.0.pdf
complete example (code and PDF): http://mvcmusicstore.codeplex.com/releases/view/64379