A number of people have reported issues with their iPhone 5 connecting to specific Wi-Fi networks. Sometimes it refuses to connect at all; sometimes it drops the connection. Some people report that even standing right next to the router with their iPhone 5 the signal strength is extremely low, but it works fine on other devices.
@Workaround@ : You can always try holding down the Home button and the Lock button together for a few seconds until you see the Apple logo and the phone restarts, but this is unlikely to be a permanent fix.
@-Solution-@ : Apple released the iOS 6.0.2 update specifically to fix the Wi-Fi issue, but it has persisted for a number of people. If you have the latest version of iOS and you are still experiencing Wi-Fi problems, you should go to an Apple Store or call support and see if you can get a replacement. A number of people have reported it as a suspected hardware issue and have been given replacement devices that didn’t have the same problem, although there hasn’t been any official recognition of a hardware issue.