You do indeed have a problem, Apple will allow you to de-authorize all five accounts once each year. You can de-authorize individual computers from each computer or device associated with that account.
I ran into much the same problem not long ago, I sold a few computers with out de-authorizing first and had to wait until the one year was up. Now everything is fine.
It will take some guesswork perhaps getting it straightened out.
The chances are very good that you have many different apps under many different accounts and that's where the error is coming from.
You can sort this out by logging in to each account in turn and looking at what has been purchased under that account, that way you can separate which can and cannot be synced.
It will also tell you what the date is that you can de-authorize all of them, I do recommend doing so as soon as you can and you may also want to consolidate your accounts to avoid this problem in the future.
Also a call to Apple at 1.800.275.2273 and talking to them, that is one part that I cannot do. It is well worth the time spent to straighten this out.