I have run across this problem more than once so I thought it was worth a mention here.

You can only authorize 5 computers to play songs you've bought from iTunes. What if one of the computers dies, or you wipe the computer and sell it to someone, but you forgot to deauthorize it before you did so?

Well once a year you can rectify it and get that authorization back. Just to to the iTunes store in your iTunes and click on your account address at the top right of the screen (under the "Search iTunes Store" field). Enter your username and password in the box that opens and click on "view account." You will see a button that says deauthorize all.

Apparently you can only do this once a year (according to the Applecare Tech I spoke with), but now you have a fresh start and you can authorize the full 5 computers to play your music.