We towed a 4600 lb. dry weight trailer with a 1997 F-150 4.6 2 wheel drive (many times with a 4 wheeler in the bed) until 2012 when the 350 diesel came along. The OP can do it based on tolerance for slow hill climbs--I went up many at 25 - 35 mph because I couldn't afford the diesel and the F-150 wouldn't die (sold it at 174K locally and it is still running at over 250K).
I don't see that the OP has said whether he has a 4 or 6 speed transmission--we had 4. With close ratio upper gears the 6 is much better for towing. It is very important with the Ford 4 speed to lock out OD (or use tow mode--depending on which is has) when towing. The older 4 speeds like ours unlock the torque converter when more torque/hp is called for running in 4th gear--this over heats and kills the transmission. With OD locked out third gear will provide all the hp necessary to run down the road 60 - 65 mph. IMHO (yours may differ), it is better for long term durability to run the engine at the higher rpm than let the transmission heat. Ford overhead cam engines will spin high rpm all day long. Now if the OP has a 6 speed with tow mode, just put it in tow mode.
One last thing, do not consider this setup without weight distribution and anti-sway. It can be done and good luck to the OP. Only problem will be the building desire for a new, stronger, truck.