SoundGuy. NICE SHEET!
Not many folks would go to this extreme effort to determine what they can tow.
I suspect after looking at the towing guide for the OPs vehicle that they MAY have enough cargo capacity for 5K loaded trailer PROVIDED they do not exceed 500 lb (IE 10%) hitch weight..
I do not recommend this since it really has the potential for an unstable tow putting the OP, their vehicle, their trailer AND other motorists at risk.
Granted, they did say 3,500 lbs empty, the problem I see with that is published dry weights are often LOW and don't include battery or propane and as I mentioned they can easily reach 500 lbs of tongue weight at 3,400 lbs at 15% tongue weight..
In effect putting them way over the max tongue weight for the vehicle once they start loading personal gear, water, and food into the trailer.
It IS entirely possible that the limiting factor might actually be the OEM hitch and hence the reason the towing guide specifically states a max of 500 lbs tongue weight.
We will never know, sadly since the OP does not wish to disclose any of the vehicles numbers like GVWR, Curb weight and or the cargo weight from the yellow sticker..
I wish the OP all the good luck they can get..