Just got a D5200. Cannot seem to get REALLY sharp images.

[Lightpath48]

I've owned a few different iterations of the Nikon kit lenses. They aren't critically sharp at the edges, but get much better at f/8 and f/11. Try mounting your camera on a tripod and shooting the same scene stopped that far down. It really helps. For a graphic of how this works, check out this link, click on the Blur Index and move the aperture slider up to f/8 and f/11. There's a considerable difference in edge performance there.