OK, I will be the first dissenter. You MAY be fine but maybe not. We need more info.
First, 6,000 loaded will be 780 lbs tongue weight plus the WDH and you are near 900 lbs. Your F-150 hitch is likely rated for 500lbs without a WDH and 1,000 with but you need to check. It's stamped on the hitch.
Second, you need to know your cargo rating If you have 900lbs TW and 600 lbs of passengers you are at 1,500 lbs of cargo. How much extra gear? Look at the sticker in your door jamb. It will say but cargo capacity usually allows for a 150 lb driver. You need to know how much cargo you have before you load the bed, load the cab, and hook up a TT.
Last, you need to know your axle ratio. The 5.0. Is rated as low as 6,900 and as high as 10,800 tow capacity. 3.31, 3.55, or 3.73. There is a code on the sticker in door jamb. You can look the code up.
I;m linking the Ford 2016 tow guide. I thought the codes were in there but I can't find them and I need to head out to work. This is a great resource for you anyway.
2016 Ford Towing Guide