Forget about all that junk.......mfg. published max tow ratings numbers from any source mean NOTHING....they are 'magical' number derived from using a base model with a 150# driver and 20# cargo.........DOesn't exist in the real world.
Have your truck loaded up camp ready (you, fuel, passengers, all stuff that is in cab and any stuff in bed)add 200# fr hitch if you don't already have one on truck.
Get it weighed........That will give you
Total actual weight
Front axle weight
Rear axle weight.
Now you have some numbers to work with.
Subtract total weight from trucks GVWR (Total weight truck can weigh)----found on data sticker on door jamb/glove box of YOUR truck.
Now you have 'payload' available to add to truck before reaching GVWR
Check out front and rear axle weights against their perspective axle ratings.
Now you have how much weight can be added to each axle before reaching the axle weight rating
Also look at rear tire max load @ max psi on sidewall of tires
Now you can 'guesstimate' how much trailer/5th wheel you can tow based on trucks actual available weight numbers from weighing.
Use 15% of GVWR for trailer tongue weight
Use 20% of GVWR for 5th wheel pin weight.
Now can you add that weight number to your truck and be within trucks GVWR, RAWR, Rear Tire Load Ratings ???????
Roughly.......
2004 2500 GVWR---9200#, FAWR---4500#, RAWR----6000#
Max tow could be 12K due to higher available payload because of gas engine (lighter curb weight vs GVWR)
So get weighed...then figure numbers.