GVWR 6800 is max weight, on the tow vehicle as it's going down the road.
Payload 1540 is weight the vehicle was rated to carry (empty, as the vehicle left the factory). Anything (aftermarket accessories, cargo, passengers, and pets) added to the vehicle, subtract from that weight capacity. Cargo includes weight distributing hitch (about 100 lbs) and trailer tongue weight.
GCWR 14000 is max loaded weight rating for truck and trailer combined.
8000 MAX tow capacity is what the vehicle is rated to tow, under the right circumstances. Those circumstances don't include accessories, passengers, or cargo.
As the vehicle gets loaded with accessories (undercoating, bed liner, bed cap or cover, tool box, floor mats, step bars, etc), people, pets, and cargo, it's available payload and tow capacity are dropping, pound for pound.
When you put the weight distributing hitch in the receiver, your payload and tow capacity drop by about 100 lbs. If you have a fiberglass bed cap, that could eat another 200 lbs. Throw in a generator, tool box, and a large family, your payload and tow capacity may not be enough to support that trailer. It's difficult for any of us to say you're good to go, we don't know who, or what, you'll be carrying.
Add up the weight of accessories, people, pets, and cargo you will be carrying. Subtract that total from your payload and tow capacity. See if you have room to carry the trailer weight.
Here's a link to a calculator that may shed some light on what to look at.
That 5970 lb dry weight will easily reach 7000 lbs, when loaded for camping. It's tongue weight could be 900+ lbs.
Average camping load (dishes, pots and pans, bedding, camp chairs, camp gear, BBQ and supplies, groceries, water, etc) is 800 to 1000 lbs.
Tongue weight is not a constant number. It goes up and down during every trip. Average is 12 - 13 percent of loaded trailer weight.
Location of holding tanks, in relation to trailer axles, can have a major impact on tongue weight. If they are directly above the axles, they have little effect. In front or behind the axles, they can add or subtract a couple hundred pounds.