Installing the IPA is only half the battle. If you open the app, it will likely still show a connection error. To fix this, you need a tweak called TubeFixer (available on the cydia.invoxiplaygames.uk repository).
Checkmate, Store!: A Cydia tweak that helps bypass the "Incompatible Version" prompts when trying to download apps from your "Purchased" history. Finding the Right YouTube IPA Youtube Ipa For Ios 5.1.1
A Jailbroken Device: You cannot sideload modified legacy apps or apply necessary fixes on a stock iOS 5 system. Tools like Redsn0w or Absinthe are typically used for this firmware. Installing the IPA is only half the battle