Have you ever road in the back seat of a large school bus?
That back seat tends to get a lot of "air" when going over bumps in the road.
The exact same thing happens with bike racks hung on the back of any trailer.
Basically there is no real safe bike rack when it is hung on the rear of a trailer.
Some folks have even resorted to DRILLING HOLES from the outside THROUGH to the inside and running a bolt all the way through. Then using that bolt as a means to MOUNT the top of the bike rack to the trailer.
The idea is to stabilize and reduce the swing forces on the rack.
Personally after almost losing a bike rack along with two bikes I abandoned the idea of hauling bikes on the back of a trailer. Just to dangerous (not just for the bike but other drivers).
In my case I bumper pull so I make a rack that sits over top of my truck bed.
In your case I think there may be a bike rack mount you could get which uses the 5th wheel mount on the trailer to attach a bike rack. If not the case perhaps consider a front mount on your truck. Or as others do, put the bikes INSIDE the trailer, lots of creative ways which are safer...