I've downloaded the iOS 6.0.1 and trying to restore with it and still, the same message "isn't eligible for the requested build" hmmph :/
i think iphone 5 you have to get 6.0.2.
also make sure you are downloading the ios for iphone 5 not another iphone
Redownload it right here.
http://appldnld.apple.com/iOS6/041-7953.20121101.Apmtr/iPhone4,1_6.0.1_10A523_Restore.ipsw
We're sure that we're running on an iPhone 4S correct? The error that you're getting occurs only when you're using an IPSW that does not match your device, either in band (GSM or CDMA) or in device type (3GS, 4, 4S, 5, etc)