There are some Fifth Wheel Travel Trailers that are light enough to be towed by your F-150 truck so yes you can Tow A Fifth Wheel Travel trailer with an F-150 as long as you get a Travel Trailer that your F-150 truck is rated to tow.
Just be sure you have good electric breaks and good breaks on both the travel trailer and the truck and the F-150 truck should tow the Fifth Wheel just fine.
I also recommend adding a transmission cooler to the truck especially when climbing hills and if your transmission is an automatic transmission.
The transmission cooler will increase the lifespan of your trucks transmission when pulling a Fifth Wheel travel trailer or any other trailers.