Can I upgrade an iPhone from iOS 4 to to iOS 5 now that iOS 6 has come out?
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.