Yikes!!!
This sucks! When buying a site I would think any debts owed by the owner would still be their obligation.
If you purchased their affiliate accounts too then this would add a new twist to things, but you are indicating that this $5000 debt exists because of a double payment and NOT as a result of fraud.
The double payment was not made to you so I wouldnt feel obliged to pay it, but the problem is the affiliate program controls the purse strings of the affiliate accounts and they may choose to charge this $5000 debt against the account simply because they can! That may leave you holding the bag unless you can get previous owner to pay back the overage.
This is a real head scratcher. The only person I know of who has experience in this area is Tovey. He buys affiliate accounts and websites all the time and may have run into this before. Hopefully he will spot this thread and respond, though you may wish to PM him too.
Please let us know the outcome.