I can't play previously downloaded music. I have deauthorized computors and reauthorized my Mac. Each time the error message "you can't authorize more thane 5 computors" How do I solve this issue?

Repeated requests to authorize an already authorized computer for store downloads typically indicates you have corrupt or incomplete copies. Backup and then delete the tracks that won't play from your library without hiding from your purchase history. Redownload using the cloud links that should remain, or close iTunes and reopen if they don't show up straight away. While downloading click the activity widget and turn off the option that allows for simultaneous downloads.

That said if you're told you cannot authorize more than five computers, rather than the computer was already authorized and has been reauthorized, then you would appear to have run out of authorizations. You may need to remove an existing authorization, or all of them, before you can authorize this one. See Authorization vs. association - Apple Community.

tt2

Hey there cincyspartan,

We understand you're experiencing an issue with authorizing your computer to play purchased music, and we'd like to assist.

It looks like you've already reviewed If iTunes for Windows prompts you to authorize your computer when you try to play purchases.

This page may also help: Authorize or deauthorize your computer for iTunes Store purchases

Cheers!