Forget about that 6200 lb towing capacity. You will run out of payload before you get there. You might be over on payload with that 5700 lb trailer.
Reason I say that is, max tow capacities are calculated with the truck having no aftermarket accessories, no cargo, no passengers, and the driver only weighs 150 lbs. As you add weight (from any of the above), your available payload and tow capacity are going down, pound for pound.
If you have more than 500 lbs (the first 100 will be the WD hitch) of accessories, people, and cargo, you don't have tow capacity for that 5700 lb trailer.