If my gooseneck rating is 14,000-lbs and the weight of my trailer is 5800-lbs then does that mean I should really only load the trailer with the difference of weight. So 8200-lbs?
Yes, if the trailer has a 14,000lbs GVWR and it weighs 5800lbs, then the carrying capacity is about 8,200lbs. It should actually have the carrying capacity specified on the same trailer tag as the GVWR.
I thought you meant it had a 14k carrying capacity because I'm not sure how you could get three cars on a trailer that can only hold 8,200lbs of cargo unless they are just tubbed out race cars. A typical car weighs in at around 3300lbs give or take, so you can probably only get 2 on there at a time.
Are you getting the 14k number from the trailer tag? Or does it have two 7k axles? A gooseneck with two 7k axles would usually be rated at around 16,800lbs GWVR (accounting for a 20% pin weight) which would give you about 11,000lbs of carrying capacity, which would probably allow for 3 cars. Again though, this would be a bit overweight for a 2500 to pull.
If it has two 6k axles, then yes, 14,000lbs total is about right and it'll probably pull just fine behind the 2500 (with two cars on board).