Nikon D500 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 D500 are the Samyang MF 85mm F1.4 Mk2, the Samyang MF 14mm F2.8 Mk2 and the Irix 45mm F1.4.
Nikon D500 doesn't have a sensor based image stabilization system but
108 of these lenses already comes with optical image stabilization.
Since Nikon D500 has a APS-C sensor, it has a focal length multiplier of 1.5x 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 D500.
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Nikon D500 Lenses with Image Stabilization
Nikon D500 Lenses with Weather Sealings