Question about Nikon AF-S Nikkor 10-24mm f/3.5-4.5G ED DX

Does this also go on my Nikon D7100?

Of course it works. Nikon has DX (APS-C) and FX (full frame=small frame). Since the D5200 is a DX camera, it can use all DX lenses and FX lenses; conversely, an FX cannot use a DX lens.