How can I authorize more than 5 computers in iTunes?

“My iTunes account says I have 5 computers authorized. I just got a new computer and it won’t let me add my iTunes account. Is there a way to authorize more than 5 computers in iTunes?”
iTunes only allows a maximum of 5 computers per iTunes Store account for music and video playback. This can be frustrating if you change computers often or if you upgrade and realize you don’t have a way to deauthorize an old computer. In the past, I’ve run into a situation where 3 of the 5 computers authorized on my iTunes account weren’t even in my house anymore. There are a couple of ways to solve this problem.

The bad news is, you can’t authorize more than 5 computers on your iTunes account. You will have to deauthorize one computer for every one you want to add up to the maximum of 5 computers. Here’s how you can handle this situation.
The easy thing to do may be to deauthorize all computers on your account and only re-add the ones you are using. This can be annoying the first time you sign in to each computer, but you might be surprised to find you aren’t really using all 5. This is what I ended up doing because I no longer had access to 3 of the 5 computers I authorized. You have to go to your account settings in the store and click the Deauthorize all button to make this work.
Deauthorize all iTunes computers
The second option is to choose computers to deauthorize one at a time. To deauthorize a single computer from iTunes, simply open iTunes on the computer you want to deauthorize, go to the Store menu and choose Deauthorize This Computer. Doing this automatically removes one computer giving you another slot to add a new computer to your account.