1/2 ton towing a 5th wheel

Gvw will not be your worst problem, pin weight will. Take the gvw for the trailer and figure on 23 to 25% as pin weight. Ignore dry weights and published pin weights as they are not real world. Take the number you got and add the weight of a hitch, passengers, equipment you added to the truck and anything else you carry and there is a good chance you will be way over your payload capacity that is on the white and yellow sticker by your door.
Even with a lot of travel trailers a 150 runs out of payload before it runs out of max tow weight. Get more truck or less trailer.

There are some trailers that might fit your criteria, never use UVW as it means no propane, battery or filled water tanks or stuff. Plus you need to a drink all of the passengers weight. Some of the newer half tons are very capable and it's not all about the engine pulling it is also about the stopping and controlling.
It depends on the terrain also hills mountains or flatland and some salesmen will lie. From a F350 owner and a city wheel.

Did you confirm the specs? Or did the seller or RV salesperson say all ok? Rare to see any 1/2 ton with a 5er.