"but the new vehicle was received only for the depreciated $5K one? Would it be recorded as a sale for a price of $10K"

The problem here stems from using the word worth. It isn't worth but Cost that you are supposed to be using. If you can get a $10k for $5k, that is basis. It doesn't matter if that $5k was "paid" by cash, trade in, or chickens. You paid $5k. There is no $10k anywhere in that transaction. The asking price of $10k became a $5k purchase. If it had really been worth $10k, they wouldn't let it go for $5k of anything.