Nikon D5200 has a Nikon F lens mount and currently there are 316 native lenses available for this mount.
The latest released lenses that are compatible with the D5200 are the Nikon Micro-60mm f2.8D, the Carl Zeiss Makro-Planar T2/50 and the Tokina 35mm f2.8 Macro DX. Beware that Nikon D5200 doesn't have an internal focus motor so it will not auto focus with old-style screw-drive autofocus (AF) lenses. It still works well with modern Nikon AF-S, AF-I and G lenses but lenses form 1980s may not autofocus on Nikon D5200.
Nikon D5200 doesn't have a sensor based image stabilization system but
107 of these lenses already comes with optical image stabilization.
Since Nikon D5200 has a APS-C sensor, it has a focal length multiplier of 1.5× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on D5200.
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Nikon D5200 Lenses with Image Stabilization
Nikon D5200 Lenses with Weather Sealings