I don't see why authorizing your computer should make a difference, but you can de-authorize all computers by goint to your account settings in iTunes. Just tap on you Apple ID at the top right of the iTunes screen and enter your password as prompted. If you do have 5 computers authorized you'll see an option to deauthorize all of them in the Apple ID Summary box.
After you choose this you will have to go back and manually authorize each computer agin. Don't abuse this. You only get to do it once every 12 months (if i remember right).
But before you do that, go to the App Store on you iPad, select the Featured page and scroll to the bottom. Are you logged into the store with the correct Apple ID? This shows in the bottom left box.