When I create a new web project with Visual Studio, I only see the templates in the picture below:
The MVC one is missing and so I can only create empty projects.>
I don't think the accepted answer works anymore. According to Microsoft here, here, and here, asp.net-5 has been re-branded to ASP.Net Core. It looks like they've taken down the asp.net-5 templates from the general ASP.Net Web Application project type. But now there's a new project type of ASP.Net Core Web Application. I don't see an MVC template for this project type, but I don't think the Core framework has been completely released yet.