First, off, I am sorry this happened to you. Paypal does suck, no question about it, but luckily it works for the most part not because of Paypal, but because most people are honest.
I think you should fight it, and don't worry about your credit. It takes more time, but you can protest it with the credit agencies, and if worse comes to worst, take Paypal to small claims court. Sue them for 5 grand. You don't need a lawyer, it'll cost you about 30 bucks, but I assure you this will get you good customer service from Paypal then. No more sitting on hold. Call your local newspaper and local news channel. Call the Better Business Bureau. But this is simply just too much money just to let it go and suffer poor customer service.
TIP for Everyone:
One of my buddies buys and sells a lot on ebay. He has a little trick he uses, which is swears by.
In his email after the transaction, he always drops in a friendly little line like, "I'll send you your money order Monday after I get back from training this weekend. (I'm an FBI agent, and we have to do annual trips to the "Farm" to ensure we are current in skills and still in good shape. It's a grueling four days, let me tell you. 🙂"
I know it sounds corny as hell, but it works. About 5% of the time the buyer or seller disappears or emails back that his wife sold the item or he no longer has the money to buy it. 5% is about the fraud rate on ebay.
It's simple and stupid as hell, I know, but it works like a charm.