There is a (non-Microsoft) NuGet package that allows upgrading the Mvc3 to Mvc4.
There is a (Microsoft) article that explains how to manually migrate from Mvc3 to Mvc4. We can read from that article, by ex:
Locate the ProjectTypeGuids element and replace {E53F8FEA-EAE0-44A6-8774-FFD645390401} with {E3E379DF-F4C6-4180-9B81-6769533ABE47}.
Now, is there something similar that allows migrating from MVC3 to MVC5?
Is there sufficient to migrate first from 3 to 4, and then re-target the framework version (to 4.5) and install the official MVC nu-get?
As an answer that someone suggested, then for a unknow cause removed, I will add this article reference for the question above:
How to Upgrade an ASP.NET MVC 4 and Web API Project to ASP.NET MVC 5 and Web API 2