Can I upgrade an iPhone from iOS 4 to to iOS 5 now that iOS 6 has come out? If I have an iPhone running iOS 4 that I want to run iOS 5, but don't want to lose Google Maps by upgrading to iOS 6, is this possible?
You can still download the IPSW files that contain iOS from Apple - here's a list of all of them. Just find the correct 5.1.1 file for your model.

The problem is installing that IPSW. The trick to make iTunes use a specific IPSW instead of downloading the latest from Apple is to hold option (shift on Windows) while clicking the Update or Restore buttons. There is a limit to how long Apple will allow installations of old versions (without using jailbreak-related hacks), so you'll want to try this ASAP.