For , there is no officially supported "verified" YouTube IPA that works out of the box because Google deprecated the older APIs used by these legacy versions. While you can find archived IPA files on sites like the Internet Archive , simply installing them will typically result in error messages.
Searching for a "YouTube IPA for iOS 5.1.1" usually refers to finding a legacy version of the YouTube application that can run on older Apple devices (like the iPad 1 or iPhone 3GS) that are stuck on iOS 5. Current Status of YouTube on iOS 5.1.1 youtube ipa for ios 511 verified