5.x has a ton of features & improvements over 3.7.1 & even 4.x. You would be missing the shorthand Lua, all the new Lua functions & data structure fields, lots of new action parts, the modern ui & cross-platform export support. 3.7.1 was windows only; both editor & export.
As for your question, I have no idea sorry. I'm not a linux user, never have been & I wouldn't have a clue where to start. Maybe SimonS might have an idea of how you can get the windows version of the editor to work on a linux machine?
A virtual machine should be valid for the windows version - you don't really need massive amounts of system resources to run the editor, so it shouldn't be an issue.