IOS – Saving video from shared photostream

Short Answer: You can't

Shared PhotoStream is a feature of iOS 6 and therefore not available on iOS 5. Some users claim they had gotten the feature working and enabled by removing and re-adding the iCloud account, however I have never seen it work.

From the official description of a shared PhotoStream (Bold by me):

Select photos directly from the Photos app in iOS 6, iPhoto or Aperture on a Mac

The Copy function copies the photo onto the clipboard. You can then paste it into other apps, say Mail, by tapping and holding until a contextual menu appears that says "Paste". If you're on a web page, you can tap and hold an image and select "Save Image" to save it to your camera roll. But you can't use the Copy function to "paste" it into your camera roll.