The sticker on the door says GVWR-5150lb.?
This has nothing to do with tow ratings per say. GVWR is "gross vehicle wheel rating" That simply means the max amount of weight that can be on the vehicles wheels. Lets say for example your truck weighs 4,000# with fuel in it and you are 200# plus you carry around 150# of junk in the bed. That would mean you now have 800# of payload capacity. Payload is anything on the trucks wheels like additional stuff in the bed, extra passengers, tongue weight of a trailer, ect.
What you need to find out is the the GCWR "gross combined wheel rating" This is rating is the max weight on the wheels of both the truck and trailer. Lets say its 9,000# for example. Now you simply subtract the weigh of the truck loaded from that and it will tell you the tow rating. This is only in the owners manual, not on a door sticker.
If you give me the year, engine, tranny type, rear axle ration, bed length, cab style I can look it up for you. I am a part time trailer dealer and have access to all this info for most stuff built in the last 15 or so years.
As for a trailer a tandem axle is probably going to weigh too much and kill your payload on the trailer. A single axle trailer with a 3,500# axle and brakes on that one axle is going to weigh about 800# so it will have a honest 2,200# tow rating. This will probably be the best you can do. I think 2,500# plus the weight of the trailer is going to be a bit much for a S-10 because you are going to be pushing the 5,000# mark by the time you add in the empty weight of the trailer.
You really need a 1/2 ton truck for this.
Chris
