> Associated devices
For iTunes to play content from the iTunes Store, your Mac must be associated with your Apple ID. You can have up to 10 devices associated with your Apple ID and iTunes Store account at any time, though no more than five Macs or PCs.
This can be problematic, as over time you might associate different devices with your Apple ID. To check how many you have, make sure you’re connected to the internet, then open iTunes and choose Account > View My Account.
When your account info appears, find the “iTunes in the Cloud” heading and click Manage Devices there. This will reveal a list of any iOS devices, Macs, and PCs that are linked to your Apple ID, which grants those devices the ability to automatically download iTunes and App Store purchases, or to redownload past purchases. Click Remove next to any device you no longer use. You should also do this if you’re selling or giving away your Mac.
To add a new Mac or PC, in iTunes choose Account > Authorizations > Authorize This Computer. Enter your Apple ID’s password; after a few moments you’ll see a confirmation.