Alpo,
Welcome!!!
As you have found like many, the limiting factor for a 1500/150 truck is the available payload. If your 1400lbs is per a website, you may not even have that much. Look in the drivers door jamb for a yellow sticker that states "All occupants and cargo not to exceed: XXXXlbs". This is the available payload for YOUR TRUCK as it rolled off the assembly line. As it states, ALL occupants (including the driver), all cargo (coolers, firewood, etc), any accessories added (step bars, spray in bed liner for example), the hitch (wdh or in your case the 5er hitch), and the trailer tongue/pin weight). Weights listed on websites are usually for a stripped down truck without any options. The more options, the less the payload.
And unfortunately the trailer manufacture "brochure" weights often times don't include options, even those options which are "mandatory". For a 5er, you generally have ~20% of the loaded trailer weight as the hitch/pin weight. So estimating your new 5er weighs 7000lbs loaded for a trip (no one toss an empty trailer), you could be in the ballpark of ~1400lbs pin weight before the 5er hitch or passengers are in the truck. To tow this trailer, pending what the family weight, weight of the hitch, and the pin weight.
Another thing the "brochure" weights do not include is the weight of the propane tanks or a battery. For 2-20lb tanks and a battery, this adds ~120lbs, and for 2-30lb tanks and a battery, this adds ~160lbs, all to the trailer tongue weight. Not 100% sure how this affects a 5er, it would imagine most of that weight goes on the pin also if the the tanks and battery are up front by the landing gear.
Best thing to do is actually weigh your truck with the family with a full tank of gas and see how much payload is available after you subtract the actual weight from the gvwr of the truck. Then you can subtract the weight of the hitch (5er or wdh) and get an estimate of what your loaded tw should be less than.
The tow ratings for the new trucks using the set standard has 2-150lb occupants, and a 10% tw while towing an open flat bed style trailer with weight on it. A tt generally needs to have 12-15% tw for a safe, stable tow which adds up quick depending on the style tt, how it is loaded, etc.
Good luck in your search.