OK, say your purchased a product at $3 and you plan on selling it for $5 to make a $2 profit.
The customer purchased the product and paid you with a fake $5.

Under GAAP, do you recorded your loses as the $3 price that you purchased the product at or the $5 that you sold it as?

Yes you should record just this entry:
Dr. Cost of goods sold 3
Cr. Inventory 3
If you previously recorded the sale entry you should reverse it.
Dr. Sales 5
Cr. Cash 5

It is as if you sold the product for free