Alright, mc5 is not part of the JA skeleton so it's left out or deleted.
I'm guessing the same distortion happens in modview, correct?.
If you moved bones of the arm/hand out of their original position it will distort the mesh when anims of those joints are triggered.
2nd cause could be a weighting error:
What happens if you select the lhand bone and rotate it in max? do the same with the rhand bone. If nothing happens, try rotating the first bone of each finger to pinpoint the problem.
Sometimes stray verts are assigned to bones we didnt intend to, or its a mistake on our part, i've had a few of those myself. If you cant find anything wrong, i can take a look at the max file.