This is the holy grail. The original YouTube app version 1.3.0 (circa 2012) came pre-installed. However, a developer known as InvoxiPlayGames created a tweak called .
After extensive testing on an iPod Touch 4G (iOS 5.1.1), these are the only reliable versions. Youtube Ipa For Ios 5.1.1
YouTube has moved from Data API v2 to v3 and beyond. This is the holy grail