The first thing that popped into my mind reading this was a Honda Civic is a pretty "reasonable" car.
Second, I'm not sure it would be that great of an idea to trade a known car, that you owe 11k on, for a 5K unknown car.
The question is, do you just not like the Honda Civic?
What would you be able to get for 5K? Used cars are ridiculously priced right now.
If you want out of the Civic, you're best bet financially is doing it as two separate deals with private parties. Is the bank that holds the title local to you?
What is the car worth? After selling it, how much from the sale would you have in your pocket?
I understand the appeal of what you want to do. But a 5K car is probably going to need new tires, brakes, tuneup, and unknown deferred maintenance/repairs.
That 5K car may end up actually costing closer to $7500.