We have a gooseneck horse trailer with a gross weight of 7000lbs. We currently pull it with a 2018 F150. It works fine. There are plenty of horse trailers that will work on an F150 with a gooseneck. There are a few 5th wheel trailers that are F150 friendly, not many, but they are out there.Pin weight on any 5th wheel is going to exceed the payload of a lightning. I wouldn't try to pull a 5th wheel with any 1/2 ton in the first place.
I think the bigger problem will be that the 5th wheel will almost guarantee you will be over payload. Ford is shooting for 2k and if they can hit it that will be on a base model. Add options and you will eat that up fast. I would bet most will have a payload of 1500-1600. Take a small 5th wheel with a GVW of 7500 - 23% you are at a pin weight of over 1700 and now you have to add people and stuff in the truck.