The MoCo did not go to 25mm wheel bearings until 2008. IIRC, the OP's '05 FLSTC has 3/4" rear axle, same size as the '99-'00 Road King. FLH models went to 1" rear axle in '02. I don't think the axle is generating the noise but have a suggestion.
Just a guess but something to check. The rear wheel inner spacer could be moving around in the inner hub if it is too short and not clamped tight between the wheel bearings. There could be a difference in length between the softail and touring rear wheel spacers or depending on how the bearings were installed, the inner spacer might not be clamped tight between the wheel bearings. The service manual includes a procedure for installing wheel bearings and, if not followed, could leave some space for the inner spacer to move around.
If the noise is cyclical, as in something making contact with every rotation of the rear wheel the OP should look for something making contact with each wheel rotation. The wheel spacing in the swingarm could allow something to contact the swing arm or the belt guard. I have experienced this myself after converting 16" rear wheel to 18" rear wheels on my '02 FLHT. I was hearing a cyclical noise from the rear wheel and found one of the rear pulley bolts had loosened up and backed out just enough for the bolt head to make light contact with the swing arm.