Look at it this way - your new car has 5 grand left to pay off, but let's say you pick up an OK car on CL for about the same price after you've sold your new car for 10 grand. 5K in the pocket, right?

This might work if you research the heck out of the used car's condition and the mileage it's being sold at.

Timing belt change because it's approaching 60k miles? Depending on car type, easily a couple hundred bucks. Brake rotors worn to limits? Almost a grand to get fixed depending on the car. Assuming calipers are ok.
Hope the transmission is ok, that's a $900 or more for a redo.

I'm not saying this won't work, but if you're going to go this route you'll need to make up for potential maintenance issues in due diligence up front, make sure the car is mechanically solid before buying it.

If you don't, or that old car craps out because it's old you could be hit with unexpected expensive maintenance issues that could make your finances uncomfortably tight after that 5 grand is gone.

Me? I'd pay off the new car and keep it. You know where i's been, its not hiding anything, and it should give you many years yet of major issue free driving. If you can make the payments in your current financial status, keep paying that payment towards debt once the car is paid off.