I couldn't find any info on your TT either. If the 5540 lbs is the GVWR, you may be OK. GVWR is the maximum the TT can weigh with everything loaded, i.e. you never want to exceed this weight. So if it's the GVWR, that would give you about 17% margin to your Ford's towing limit.
However, you also need to worry about payload, which is usually the first thing to be exceeded. Open your Ford's drivers door and look at the sticker you find there. It will tell you how much weight you can add to your Ford. This is the payload. It does not include the driver, but it does include EVERYTHING else you may add. This includes the tongue weight of the TT and the weight of the hitch itself. (Weight distributing hitches, which you WILL need) can run 50-75 lbs.)
So now you need to figure tongue weight. I was unable to find any numbers on your model TT. So you'll need to ask what the tongue weight is. The tongue weight they give you will most likely NOT include a battery on the tongue OR the propane. So you'll need to add that weight to the tongue weight. Alternatively, you can figure about 15% of the GVWR number once you figure what it is.
Once you know your tongue weight, add the hitch weight and everything else you intend to add to the Ford. If this number is greater than the number on the drivers door sticker, you have a problem.
Note the biggest lie RV salesmen say: "Oh, a half ton pickup can tow this!" Not all half tons are created equal. My 2009 Silverado owners manual listed 99 (yes, 99!) permutations of engine, cab, bed, rear end gearing, etc. The tow capacity for these ranged from 4000 lbs to 12,000 lbs. So how can an RV salesman truthfully tell you that YOUR pickup can pull any specific TT?
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10