Hello pitzkc,
Thanks for asking the Apple Support Communities for help with authorizing your computer, and the alert that there are already 5 computers associated with your account.
The easiest option is to deauthorize all computers associates with your account, and log back in to the one you are currently trying. This article will help: Authorize or deauthorize your computer for iTunes Store purchases - Apple Support
- On a Mac, open the Music app, Apple TV app, or Apple Books app. On a PC, open iTunes for Windows.
- From the menu bar at the top of your computer screen, choose Account > Authorizations > Deauthorize This Computer.
- Sign in with your Apple ID.
- Choose Deauthorize.
If one of your 5 authorizations is on a computer that you don't use anymore, deauthorize it. If you sold or gave away a computer that's used one of your 5 authorizations, you need to choose Deauthorize All on the Account Information page. Then authorize each computer that you still use."
Thanks and have a wonderful day.