Use the Safari Web Browser . Navigate to youtube.com . While not as smooth as a native app, the mobile web version is updated by Google and will actually allow you to log in and watch videos. You can tap the "Share" button in Safari and select "Add to Home Screen" to create an icon that looks and feels like an app.
Sites like Momentum Dev's Store often provide "cracked" or fixed IPAs that are compatible with older signing methods.
Since modern iTunes and Finder versions have removed App management, you’ll need specific tools to move the IPA to your iOS 5 device:
iOS 5 lacks the modern security certificates required to talk to today’s servers. 1. Finding the YouTube IPA (Version 1.1.0 or 1.2.1)
This tweak redirects the app's requests to a modern server. Add the source http://cydia.skyglow.es/ in Cydia and install "Tube Repair Beta".
If you prefer not to jailbreak, you can use the web version. Open Safari and go to m.youtube.com.
To make it work, users must generate a personal YouTube Data API v3 Key via the Google Cloud Console.