I towed a 19K pound 5th wheel with a similar 2005....5.9, 3500, 6 speed, 3.73, SRW, chipped. The 5.9 is a brute, no surprise here, and it had no problem pulling, or handling in curves or grades...uphill. Downhill was a different story. The first time out, down a loooong 6% grade in AZ, we ran out of brakes....sure the trailer had brakes, but it was asking too much of the Dodge to slow it down, with 19K pounds pushing. We added an exhaust brake and that improved planned slowdowns, like grades....it did nothing for panic stops. Shortly after, we migrated to a single axle Kenworth that had 24" tires. larger brakes... more rubber on the ground, and a 3 stage Jake...towing/stopping/weight problems solved.
Regarding manufacturer stated weight capacity....remember when changing the rear end gearing to a 410, or lower, all that does is change your ability to start easier from a dead stop....it does nothing to increase your load carrying capacity, regardless of all the hype.
Stay with a "reasonable" size RV with a light duty truck....If you want bigger/heavier, go with a MDT/HDT for piece of mind/safety.
Regards
Gemstone