Since I was of driving age in the time frame you're asking about, the cars will pull a trailer with a car on it. The biggest limiting factor is a trailer hitch that attaches at least 4 points to the rear frame, since the frame aft of the rear axle on the cars is lightweight compared to a truck frame. It is dependant on the trunk floor, and body mounts for rigidity. Having a sturdy hitch will compensate for the rather weak frame structure behind the rear axle.
Tongue weight is also going to be a factor, as the rear springs of a car will not support anywhere near the tongue weight that truck springs will.
You can add airbags to the car springs to support more tongue weight, or use a hitch with torsion bars, called a weight distribution hitch, that pushes the load further towards the front of the cars chassis.
The transmission in a 64 GP isn't really the ultimate for trailer pulling duty. The slim jim was barely adequate to move the cars around, let alone tow a trailer, with another car on it. I'll add that most people that towed cars back in that era, used a tow bar, and flat towed their other car, car trailers were for the elite back then.
One other point is 4 wheel drum brakes on the GP, they will always be prone to fading. The stock system is activated by a single master cylinder, if you have a hydraulic failure, you're pretty much along for the ride. I would also want a trailer with brakes on both axles to preserve the tow vehicles brakes as much as possible.
By the time you make the modifications to the car, you might justify the purchase of a truck that will pull a trailer with little, to no modifications.
I'm not trying to disuade you, just laying out the facts that you would have to address on a 64 GP to pull a 5-6000 lb loaded trailer. I use all of my cars to pull trailers, and tow dollys, people really look at you funny when you're pulling a 92 Grand Am, on a tow dolly, with a Vibe down the interstate......
I've also used my 2005 GTO to pull a tow dolly with a 97 T/A on it, as well as an enclosed 10X6 foot trailer, with all our T shirt paraphenalia when we used to sell T shirts at many of the Pontiac events. A tow dolly is a lot lighter than a 16 foot trailer is, the reason I own them, rather than a trailer. I installed air bags in the rear springs of the GTO, because it squatted too much when hauling the loaded trailer.
Every vehicle I own has a trailer hitch, and I use them to tow with, but I try to match the horse, with the cart.
I also own a K3500 dually to haul anything that is going to overtax the cars. As Clint Eastwood/Harry Calahan said, "A man's gotta know his limitations", the same thing goes for your tow vehicles.