John--Just realized, in re-reading, that you did say how old your son is. If he is fit, Cabin Flats is probably doable. However, I'll posit some other destinations. SAmmcdonald's suggestion is a good one. On the N. C. side, you might want to consider Bearpen Branch on Noland Creek or Bumgardner Branch on Deep Creek. I took my daughter to both when she was around your son's age, and she handled it just fine (of course her mother slipped and broke an ankle at the latter site, something which occasioned quite a bit of trouble before we dealt with it after a harrowing and painful night for her).
In the Bradley Fork drainage, you might also want to consider Chasteen Creek. Over in the Cataloochee area, Pretty Hollow is 1.9 miles from the trailhead and is a lovely place.
There are, obviously, lots of possibilities, and my apologies for missing the obvious on the lad's age the first time around. Hope this helps a bit.
P. S. I personally think 5.5 miles could be a bit much, but by that age I had made half a dozen trips to the Bryson Place, and that was when the Deep Creek Trail still featured more than a dozen fords. That's about the same distance as what you are contemplating, and the going on Bradley Fork is basically fairly easy (unless you are old and overweight, like me, then it is arduous--but I plan to go there in the spring).