I don't think they had the yellow payload sticker in 2001?
At any rate, you'll get down the road. Just don't be surprised if it's in 2nd gear on the grades most of the time and only in 3rd cruising on the flats.. You might get into OD if you have a tail wind, but for the most part, you will need to let the engine rev to keep it in it's power band.
Towed a #5000 TT with a 97 F150 5.4 and 3.55 gears and it pulled fine.. Was over it's GVWR when hitched up, but did well for over 12 years and 255,000 miles..
Just don't be afraid to rev the engine.
Good luck!
Mitch