If you need to authorize your new computer and are unable due to already having five authorized computers, and you no longer have access to old computers to deauthorise them, you can deauthorize all computers by doing the following:
- Open iTunes on a computer
- From the Store menu, select “View my Account…”
- Sign in with your Apple ID and password.
- Under “Computer Authorizations” select “Deauthorize All”.
- Authorize each computer you still have, as you may require.
Note that You may only do this only once per year.
After you “deauthorize all” your authorized computers, authorize each one as required.