Is there an inhabited planet within 5 light-years of Earth?

Yes there is! It's called Akart and you can read about them in Contact Report 035. The Akartans have been coming here to gather food for quite a while already.

Their planet is massively overpopulated with over 23 billion humans which is probably how planet Earth will seem in about 100 years if we continue on our current path to "go forth and multiply".