Before upgrading to Silver for posting pictures, I'm going to work on this a bit. Although even at high shutter speeds or with stationary objects the softness seems to be there, I think you might be right about the poor holding techniques (much as that wounds my pride). Tonight I've taken some shots and they seem to be better, but they've been at closer range. Also, the soft ones were JPG, the sharp ones RAW (NEF). I'll try some longer distance shots when the sun is back out and see how they come out.
Still not sure where that 35 mm equivalence issue (35mm equivalence = actual focal length) is coming from. I use Aperture 3, maybe it has an problem with D5200's; I know it hasn't been upgraded to take D5200 RAW (NEF) images yet.