As mentioned base curb weight listed of 5000 lbs will be under actual weight. However, using this let's see how the numbers add up.
Assuming weight evenly distributed between both axles puts 2500 on back axle. With a RAWR of 3800 that leaves 1300 left on that axle.
My trailer weighs 6500 dry and ready to camp is 8000 so there is 1500 worth of options and gear and no toys (not a toy hauler). If we use these comparatively low numbers for your proposed rig you start at 7000 but will be more like 8500 (before toys). Use a tongue weight of 15% of 8500 is 1275 leaving you 125 payload remaining on your rear axle before passengers or cargo. This is assuming the base curb weight (which is likely low) and you are not exceeding 15% of the tongue.
This may also be exceeding the hitch rating. The 2011-2014 was 1150 or so. What the does the sticker on the hitch say for the 2015 F150 for max hitch weight?
Good luck,
Stu