You said you have the 6.0 gasser. Is your axle ratio 4:10 or 3:73? If 3:73, the max trailer weight you can tow is something like 9600 loaded. If 4:10 it jumps to around 13,600.
The loaded pin on that fiver is going to be around 2600 lbs. Add 150 for hitch, 500 for passengers and gear and you are going to be over the gvwr of the truck. Anything else in the bed of the truck, tools, firewood, etc will put you way over gvwr.
Lots of people tow heavy fivers with 3/4 trucks but I would consider a lighter fiver or a 1 ton truck.
I have been in this boat and was not comfortable towing over weight so I moved to a one ton. I now have room to spare.