The last compatible version of the official YouTube app for iOS 5.1.1 was YouTube 1.3.0 (or similar versions from 2012-2013). However, this version relies on legacy Google APIs that have been shut down for years. As a result, even if you install it, the app will likely show an error message ("Connection Error" or "Update Required") and will not play videos.
Here is the story of how you can breathe life back into that classic glass slab. The Problem: The "Version Mismatch" Wall youtube ipa for ios 511
In Cydia, add the repository: cydia.invoxiplaygames.uk/beta . The last compatible version of the official YouTube