I would HIGHLY recommend you break out your owners manual and read it.
My 2009 Silverado manual listed 99 (yes, 99!!) permutations of the 1500, based on engine, transmission, cab size, bed size, towing package, rear end gearing, etc. The towing capacity of these 99 permutations ran from 4,000 lbs to 12,000 lbs. So unless your RV salesman asked you SPECIFICALLY which Silverado you have (yeah, right -
) I wouldn't believe a word he says. I'd also be leery of anyone on this forum, too, because they don't really know which Silverado you have, either.
You need to find out what the REAL tow capacity of YOUR specific Silverado is and go from there. Also look at the payload limit that's on the sticker on the B-pillar of your drivers door. Anything you add to the truck except the driver is payload. This means wife, kids, dog, stuff, trailer tongue weight, WDH, etc.
Good luck. As one point of reference I pulled my Mini Lite 2503S for 1-1/2 seasons with the 2009 Silverado in my signature below. It was rated for 7,500 lb towing. It was OK, but I'm in the flat Midwest. I did not want to take it in any real mountains, so now I've got a 2500.