The '01 Mounty with the 5.0L and all wheel drive was rated to tow a maximum of 4535 lbs with the 3.55 gears (GCWR of 10,000 lbs) and 4990 with the 3.73 gears (GCWR of 11,000 lbs).
Running a lightly-loaded vehicle with a half tank of gas and nothing inside but a skinny driver, it *might* barely make it at 5100 lbs... but just barely. At that point, it'll be right near, if not over the GCWR and the max trailer weight. Axle weight without a weight distributing hitch will likely be WELL over their maximum. On my Sport, with a much shorter rear overhang than your Mounty, a mere 300 lbs of tongue weight put me within 50 lbs of the rear GAWR.
IMHO, it's too much for the truck. It will not be a pleasant towing experience. If you're going around the block with it, I might say give it a try. If you're going cross-country or through the hills? no way!
-Joe