The very best way to do this is to load your truck of all gear, people, hitch, etc. and go to a truck scale and get both axle weights and total truck weight . First, take that total weight and subtract it from the GVWR value on your driver door jamb number found on the sticker. This is your remaining payload capacity and is used to determine the maximum trailer weight you can tow.
On a very general basis, trailer tongue weights are about 15 percent of the total trailer weight. So let's say your remaining payload capacity from above is 1,000 pounds. Your maximum trailer weight would be 1,000 / ,15 = 6,700 pounds (rounded). Of course very important to not improperly load trailer by putting more "stuff" behind trailer axles to game the tongue weight (artificially lowering it) because you will fishtail like crazy. Having a good weight distribution hitch is critical.
That is best way to figure out your capacity, especially with a 1500. You can look up payload capacity on Ram website for your truck (charts only give best case scenario, they don't speak to your specific truck) but it does not take into account any aftermarket accessories, bigger tires, gear and people, etc. so you end up having to guess at how much all that weighs. But if you don't have scales available to you, this number would be useful to start at and then you have to analyze all your add-ons and stuff and figure out whether to subtract from that base payload capacity number. Will get you to same place, but it will be a estimated remaining payload capacity so be aware. I will follow up with VIN search link, the one u had is broken, again.