Towing with 1/2 Ton Suburban or Yukon

We are getting ready to buy a new tow vehicle. New to us anyway. We are looking at late 90s or early 2000 Suburban 1500 or Yukons. Everyone tells me this v8 5.7 engine is big enough to tow our 5200lbs dry camper. BUT I have found different tow capacities online. Recently I had someone snap a picture of their box under the truck that is part of the tow package and it said the hitch was rated 5000lbs max. Does anyone else tow with a 1/2 ton? It just seems like this should be more than enough power and brake to tow a 5200lbs camper but the online manual seems to be less than I thought.