An F250 has a max GVWR of 10,000 pounds. Virtually every 5er outside of some of the 'Lite' versions will exceed that weight on the truck.
If it is a CC long bed, the truck will weigh in at over 8000 pounds with fluids, etc. Add you, mom, the kids, dogs, hitch, a bed full of whatever, you might have a pin load capacity of 1000 pounds.
The question you will now ask - will my 6.7 powered truck haul a 12,000 trailer, 2500 pound hitch weight. Absolutely. Will it do that job safely - maybe. Will it do it legally - nope, though I have been doing it since 2011 as my truck by acual part numbers has a 12,100 pound suspension and I will continue to haul our 5er, this sites weight police not withstanding
Ford F250 6.7 Lariat CCLB, 5er Hitch Option w/ Rite air bags,
Montana High Country 343RL (sold it!)