Tongue jacks on travel trailers are almost universally at the point where the two main beams of the tongue come together in a "V" directly behind the coupler.
They are almost always either in the way of the tailgate, or VERY close when the truck and trailer are in a straight line. As soon as you turn a little, *CRUNCH*!
If you've got room you can install a different kind of jack off to one side, but the WD brackets, propane tanks and/or battery may be in the way. Then you still may contact the propane tanks or battery box in sharper turns.
Believe me, you do not want to have to constantly worry if you are turning too short, because eventually, you will turn too short and damage something. It is not fun.
A hitch extension long enough to clear the tailgate would derate your receiver too much. It is probably already pushing its limits with a normal length shank.
Do you even have payload capacity for one or two bikes in the back of your truck? With a 5' bed it is an F150 or 1500 series truck with a payload of 1500lbs at most. 2/3 of that is used up on the trailer tongue, and most of the rest is people in the cab. So no, there are not really any feasible options with what you have.
You need an F250 or 2500 series truck with enough payload capacity for the bikes, and a bed long enough to load the bikes with the tailgate up. I'm sure you probably use the current truck as your daily driver and you don't want a bigger truck, but then you don't get to bring the bikes with you on camping trips. It's that simple. You have to decide what's more important to you and make a compromise.
