My account shows 4 devices, I want to authorize another computer. When I try to authorize it says I already have 5 devices.

"Deauthorize All" and then authorize any computers you still have and want to use. See the Deauthorize All button in the second screenshot below from Authorize or deauthorize your computer for iTunes Store purchases - Apple Support

See your authorized computers

To automatically sign in to your Account Information page from your computer, click here. Or follow these steps:

1. On a Mac, open the Music app, Apple TV app, or Apple Books app. On a PC, open iTunes for Windows.
2. Sign in with your Apple ID.
3. In the menu bar on your Mac or PC, choose Account > View My Account.
4. 
5. Sign in with your Apple ID.
6. On the Account Information page, scroll to the Apple ID Summary section. You'll see the number of computers that you've authorized with your Apple ID. You can’t see the names of those computers. If you haven't authorized 2 or more computers, you won't see this section.
7. 

If the number of authorized computers listed is more than what you expect, you might not have deauthorized the computers that you no longer use, gave away, or sold. You need to deauthorize all of your computers and then authorize each one that you still use.