The dove photo does seem to have the VR turned on at 1/640, if you're north of 1/200 you should generally have it off, and always above 1/500th. This won't matter much on the D5000, but on the D5200 you can get slight artifacts from it.

I definitely agree though that the extra pixels are what's showing your softness: if you're pixel peeping, there's the problem, but your old D5000 hid it because it didn't have as many pixels.