Here's some figuring data.
The max payload on an F150 ranges from 3100 down to 2300 depending on model selected with max towing package.(Regular cab 2wd to Supercrew 4x4)
From the payload subtract the weight of the passengers, fuel, hitch, and whatever else you haul in the PU, not the trailer. Figure 600lbs which leaves 2500-1700 lbs of payload.
Using the GVWR of the trailer you are looking at take 25% for the hitch weight. Back figuring from that a 5er that has a GCVW of 7,500-10,000 lbs would be about right.
Those numbers would put you in the 25' range.
I know F150's pull bigger 5er's every day as I'll probably hear about but I'm giving you realistic numbers from the charts.
FWIW the CF285 in the picture ready to roll (no water)has a hitch weight of ~2500 lbs(actual) and trailer axle weight of 7800 for a gross trailer of 10,300. In theory a F150 properly equipped would handle it.
Have fun shopping. I actually went at it backwards. While looking to upgrade my 1/2t GMC that was pulling a 25' BP I found a super deal on the F350 and bought it. Then some time later I traded for the 5er. The F350 will handle a lot more which gives me upgrade room later. We liked the layout of the trailer and it fit the pocketbook.
FWIW the F350 squats about 2.5" when hooking up the trailer and is on the overloads.