There is a trick for backing a 5th wheel (actually works with TT also) to prime the turn when backing into a spot.
- When you pull up move as close to the side the spot is on as possible.
- As the back tires of the truck get in front of the spot, turn hard away from the spot.
- Continue until you run out of room.
- Turn hard the opposite way and continue until the truck is parrallel to the road.
You may have to play with exactly where you start the turns but this should leave the trailer angled towards the site and at an angle to the truck. This gets you past the slow start to turning so you can quickly bring the trailer around in a tight site.