Why can't I add a new computer to my account. I don't have 5 computers authorized?

If you see a message telling you that you already have five computers authorised, they must be old ones you have disposed of, or your existing one if it has been repaired.

In either case, go into your iTunes account and use the De-Authorise All option to remove all computers, then use the Authorise option to authorise the new computer.

Note that there is a limit to the number of times that you can use the De-Authorise All option each year. If you have reached that limit, I would expect a message telling you that and in that event, you will have to seek assistance from the iTunes Store staff.