Cannot associate Apple ID with new MacBook AIr

Question

I just purchased a new MacBook Air and have all of the latest updates done to it.  I try to associate my Apple ID to the computer and get an error message saying I have reached my limit of Authorized computers 5 out of 5.  I went into my account and clicked on Manage Devices, but I only see 1 MacBook listed as a device (a previous computer of mine), the others are iPads & iPhones, which totaled more than 5 to begin with.  I tried deleting/unauthorizing a few of these devices and tried registering my account again on the MacBook Air, but am still getting the error message.
Is there any other place that I can unauthorized computers on my account? I am thinking I may have an old PC or Mac associated with my iTunes account (that I no longer have access to and has since been recycled).
I only see that one Mac on my account under devices, so according to that, I should have the ability to add 4 other computers, unless I'm missing something.

Answer 1

Hi jmcaninch,
I apologize, I feel there may be a bit of confusion regarding authorizing a computer vs. associating a computer/device, which are two similar but seperate processes. All Associated computers/devices are also Authorized, but not necessarily vice versa. There are different limitations on each, and the Manage Devices screen will only show Associated computers/devices, not Authorized computers. For more information and clarification, you may find the following articles helpful:
Authorize your computer in iTunes - Apple Support
iTunes Store: Associating a device or computer to your Apple ID - Apple Support
In particular for your specific issue, you may find this portion from the first article helpful:
What happens if I run out of authorizations?
If one of your 5 authorizations is on a computer you don't use much anymore, deauthorize it. If you've sold or given away a computer that used one of your 5 authorizations, you'll need to deauthorize all of your computers and then re-authorize each one you still use.
How do I know how many computers I've authorized?
If you've authorized more than 2 computers, you can see how many are authorized.
Open your account in iTunesand sign in with your Apple ID. (Or, open iTunes, click Store > Sign In, and enter your Apple ID and password.) In 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. 
Do I need to authorize my iPhone, iPad, or iPod touch?
No. You don’t need to authorize your iPhone, iPad, or iPod touch, but you do need toassociate your iOS devices with your Apple ID. Your iOS devices don’t use your available authorizations.
Regards,
- Brenden