Does Visual Studio 2015 support the older versions of MVC?
Yes, It support them just after a migration (for adding/supporting new features in IDE like Intellisense and etc).
how do you create new solutions using the older MVC versions in Visual
Studio 2015?
This is not an intellectual action since the newer platforms have a lot of fixes and advantages rather than prior ones. Unless, you may be forced to use an older one due to lack of hosting support, In this case you can't Create an older version of MVC project by the IDE (VS 2015) itself, unless by adding older assembly references and some handy works in configuration based on your complete awareness of older required files and architecture, since the newer IDE usually don't have the previews references.
Note: The VS 2015 is just an IDE (Integrated Development Environment). You can run any MVC version on it (with above considerations), But the IDE's new features will be limited likely. For example, the result of MVC 4 migration in VS 2015 will be:
ASP.NET MVC 4 projects have limited functionality in Visual Studio
Next. Commands such as Add Controller, Add View, Add Area, and Go to
View/Controller are not available. Intellisense for Razor (CSHTML and
VBHTML) files is limited to HTML markup. Please see
http://go.microsoft.com/fwlink/?LinkID=320968 for additional
information on how to upgrade an MVC 4 project.
Which suffers from the lack of Intellisense and etc. But you can still run/develop the project with it or another IDE like Visual Studio Code and debugging the projects will make sense here.