Straight from Ford:
http://www.ford.com/resources/ford/general/pdf/towingguides/13flrv&tt_f150.pdf
Summary of what the link says if you read all the fine print:
5600 lbs with a weight distributing hitch system. (and one 150 lb driver and no cargo)
5000 lbs without a weight distributing hitch (and one 150 lb driver and no cargo).
*****Fat drivers over 150 lbs, any passsengers added, any cargo added to the truck bed must be subtracted from the towing weight limit.
Note 1: Camper or flat deck trailer does not mean a hill of beans difference on what you can
legally tow on a bumper pull trailer. Only the weight is a factor from the
legal perspective. That said a 5000 pound flat deck load will pull more comfortably than a higher profile 5000 lb camper as the camper is breaking much more wind and you get the parachute effect that increases exponentially as speed increases. (Similar to when you roll your window down at 60mph and stick your hand out the window. There is very little wind resistance when you point your fingers forward and a whole bunch more wind resistance when you point your fingers to the sky). So while the 5000 lb flat deck trailer will be a more pleasurable towing experience the camper is still legal to tow.
Note 2: Electric trailer brakes (or hydraulic surge trailer brakes) are pretty much mandatory on anything above 1500 lbs weights, but the actual limit varies from local government to local government. Regardless you want trailer brakes on at least one axle as stopping is always the hardest thing to do instead of going so this should not be overlooked. (electric brakes require a controller to be installed in cab of truck. hydraulic surge brakes are built into the tongue of trailer)
Note 3: While the weight distributing hitch only increases your towing capacity by a mere 600 lbs it is not because of your chasis or truck brakes, but is such a small benefit due to your little motor. The weight distributing hitch limit keeps increasing as the motor gets bigger (more hp) or rear axle ratio gets bigger (better for towing). Still 5600 lb rating is not too shabby for a little 3.7 l V6. I pulled 5000 lb similar trailer loads back in the day with a 1992 chevy 4.3 v6 and then later a 2001 chevy 4.3 v6. Never had an issue with either.
Note 4: When you simply have to carry more stuff; Put any added weight in trailer instead of the truck bed if possible. Weight in the trailer then you do not have have to subtract from your legal tow rating. Weight in truck bed then you must subtract. Added weight in trailer only increases the load on your truck's rear axle and tires by 10% or that load. Conversely, same weight placed in truck bed increases the load on the truck's rear axle and tires by 100%.