2017-2018 Silverado 2500HD / 3500HD

Dealer websites and sales people..a crapshoot for accuracy. Try this - https://www.gmfleet.com/content/dam/gmfleet/global/master/nscwebsite/en/Home/Resources/02_pdf/2017-chevrolet-trailering-and-towing-guide.pdf

Have you gone to chevytrucks.com or whatever Chevy calls it and look at the specs. You could also try looking for the Trailer Life Towing Guide. My 2016 F350 is rated for 15,500 lbs I beleive. I think the ratings have gone up due to the aluminum body. Not sure where Chevy is. Now if you want a dually I am sure you wont have a problem

2017 Chevy diesel Crew cab, 17,200lb fifth wheel capable.

http://www.chevrolet.com/byo-vc/client/en/US/chevrolet/silverado/2018/silverado-3500hd/features/capabilities/?section=Powertrain&section=Trailering%20%26%20Payload&styleOne=391274&engineOne=L5P&bodyTypeOne=3&driveTypeOne=4WD

You are pushing the SRW/DRW territory. Just because it says 16K does not magically make the weight stop there!

VERY common for 25 percent pin as in the weight pushing down on your truck can EASILY be 4,000#+.

Our 5er has a 21k rating and it weighs 23K with 25 percent pin!!!

Here are my numbers.
2017 Silverado LT 3500HD Duramax Crew-Cab long-Bed DRW
5th wheel tow rating 22,700 lbs
Cargo capacity 4,500 lbs Taken from actual stcker on door jamb
I pull a 42’ 16,100 lbs of 5th Wheel with a pin weight around 3,000 lbs
This leaves me 1,500 lbs of stuff I can put in the truck beside the driver.

clicky link
Use this for GM truck. Its their holy bible for size and weight.
Click on year model and order info..
click on chevy trucks...
then top right hand corners click on Silverado HD....
This shows lots of info on options/weights...spend some time looking them.

Then click on "model and options weight calculator".
This calculator figures all trucks front and rear axle weights from your selections. Eliminate guess work how much weight the truck can carry and how much it can pull.
Play around with it for a while. Lots of tech info on the different RPO packages.

I would get a DRW for that kind of weight, and you are used to driving a wide rv.

I tow a 16,500 gvw with my 2015 Silverado dually. Works very well and we couldn't be happier with it. That is well within our rated load which is 22,000# I believe.

B.O.

My 2016 F350 was rated for towing a 15,700 lb 5th wheel which is very close to the weight of my trailer. It handled that weight extremely well. I'm sure the new diesel SRW Silverado would handle a 16000 lb 5ver even better....the '17 GMC 4x4 Crew Cab Duramax SRW regular box is rated for a 17,200 lb fifth wheel.

2017 GMC towing guide

I tow a Voltage 3200 toy hauler, GVW for the trailer is 16,000 lbs. I started out towing with a 2003 Silverado 2500 HD. When fully loaded for vacation, the trailer weighed about 15,300 lbs, 2,500 lbs on the pin, and the truck (9,200 lbs GVW) Was about 200 lbs over the GVW, but well under the rear axle and tire maximum weight ratings. I was also right at the maximum combined vehicle weight rating of 22,000 lbs. Towed the toy hauler over 18,000 miles with no drama, but you could always tell that the trailer was back there.
In January of this year, I upgraded my tow vehicle to a 2015 GMC Sierra 3500 dually crew cab long bed and have towed my Voltage about 8,000 miles since then. The 3500 is head and shoulders above the Silverado 2500. I hardly know that the trailer is back there, and I am a lot more relaxed at the end of the day.
While the new 2500 series pickups have a higher GVW than my 03 did, you won't have much wiggle room as far as weights go with the size of trailer you are contemplating. Also, real world weights are generally higher than advertised weights for both the trucks and trailers.
If you really don't want to drive a dually, I would suggest a 3500 single rear wheel.