I will be traveling north and will be in this area around mid June. On our last trip in 2010 the road between Chicken and the Tetlin junction was washed out and was closed. Since we were on our way so...
With the exception of a few miles just north of Chicken, this road is wide, so the size of your rig shouldn't be an issue. While this road is maintained pretty well, the quality of the surface will depend on what has happened since the last time it was graded.
That said, the road from the Jack Wade junction down to Eagle has some pretty hairy sections, so I'd suggest leaving the 5th wheel somewhere and making that a day trip with just the truck.