According to the the System requirements for EPiServer 7.5 CMS, MVC 5 is supported so I would be very surprised if 8.2 didn't support MVC 5.
I have used it with MVC 5 and it worked fine and I have also added a feature request for the visual studio extension that it should use mvc5 instead of mvc4 and they are going to change that.
It deffintly works with MVC5 make sure you have the corrent versions in your diffrent web.config files. Both the main file in the root but also for views. I have had the problem with visual studio not updating al the config-files when upgrading.
I would sugest you install a new empty website and upgrade that one to MVC 5 then diff your config-files. When I get these kind of errors I always fallback to checking an defualt installation website. From time to time you can get strange error and ending up with the need for installing stuff on your computer that are missing. A default installation should work.
Can you please let me know if Episerver 8.2 version is compatible with ASP.Net MVC 5. We are in development phase and initially we have ASP.Net MVC 4 in our project. Everything worked fine. However, post ASP.Net MVC 5 upgrade, the edit mode content tree is not loading. It loads up empty all the time. However, admin mode works fine and the default home page loads up on the right hand side.
Below is the web.config setting, in case if that is helpful: