So I know I'm in NH and not MO but figured this may help. My state registers the vehicle as a Passenger vehicle (does not list car or truck on registration). It has based on a 6160GVWR which is what the sticker says on the vehicle. It doesn't matter whether it can tow 5,000lbs or not because you pay for the weight of the trailer during its own registration.
If you look at the sticker on your driver's door, it states the vehicle is a "truck" per Ford.
Example: My F350 is rated at 11,500lbs so that's what I pay for despite my truck weighing 8,400lbs (and capable of towing 16,300lbs). What I can tow has nothing to do with the truck registration. My 5th wheel weights 11,400lbs so when I register my trailer, I pay for the 11,400lbs on the trailer registration.
If your state handles registrations completely different, disregard everything I said lol.