Depends on the 5er....
I've seen ones that are basically the same size as a 12' cab over camper, so they are probably only around #4000 or so.. Others are ones that I can fully stand up in the front bedroom area and I'm 6'3" tall! Those come in at around #14,000 or so..
The 'problem' with 5ers is the pin weight.. They are usually 20-25% of the trailers total GVW.
When my Dad found the 5er he wanted, it had a 'dry' pin weight of #2500!! He had a nice Dodge 2500 diesel, but even it didn't have the capacity for that.. He sold it and got a dually Dodge diesel and is maxed out on it! (yeah, I know it's a Dodge, but he really likes that Cummins diesel.. What can I say?)
I'm guessing you have a '04 or newer F150 because you mention the 4R75 trans, so you probably have a GVWR of around #7200.. Not bad, compared to my weak #6250 GVWR, but your truck weighs more then mine to begin with.. Once you load up that bed with a #200+ 5er hitch, load up the spouse and any other stuff, you will be lucky to have around #1200 of payload left.. That's only a #6000 GVW 5er you will be looking at... (not much bigger then the 12' cab over camper!)
So, all of this means, you WILL exceed at least your GVWR and or rear GAWR before you exceed any "tow rating" figure if you go the 5er route with an F150..
Sure, people do it all the time, but if you are in any way concerned about the 'other' weight ratings besides the 'tow rating', then you might need to consider a 'bumper' pull trailer.. Tongue weights are in the 10-15% range there...
Good luck!
Mitch