Your mythical 5000 lb max tow capacity, is what the marketing folks say your Jeep could tow, with the propper equipment, and without any passengers or cargo.
Even with a propperly equipped vehicle, when you add people and cargo, that tow capacity goes down, pound for pound.
In the real world, that max tow capacity is 5000 lbs, minus the weight of everything and everybody, you put in or on the vehicle.
The average load (dishes, pots and pans, camping gear, BBq, groceries, and water, etc) in a trailer is 800 - 1000 lbs.
Unloaded weights are notorious for being inaccurate. Many times, they don't include batteries and propane.
Looking at an unloaded weight of 3567, you're probably looking at more than 5000 lbs, when loaded for camping. With a passenger (or two or three) and some cargo, your true tow capacity could be well under 5000 lbs. I think, your concerns are quite valid.