You have a 6500 lb tow rating - which means you can add at least that much weight to the curb weight of the truck. Load heavy, and even 5000 lbs for your 3700 lb TT would seem high. I can't imaging you fitting the other 1500 lbs into the truck. You have ~630 lbs of hitch weight available, your 560 is fine.
Where there's an issue is frontal area - Nissan's rating is only 30 sq ft. That's teardrop camper size. But that's only a performance issue, not a safety one (unless you find yourself going up a mountain Interstate at 30 MPH). It may be an error in the Owner's Manual - my Xterra is rated for 60 sq ft. Or maybe the 30 sq ft is just based on everything else being maxed out and you're just fine. Ours have basically the same engine, but the X is rated 5000/500, which is pretty close to what you're at.
