Nikon 1 J5 has a Nikon 1 lens mount and currently there are 13 native lenses available for this mount.
The latest released lenses that are compatible with the J5 are the Nikon 1 VR 10-30mm f3.5-5.6 PD-Zoom, the Nikon 1 VR 70-300mm f4.5-5.6 and the Nikon 1 AW 10mm f2.8.
Nikon 1 J5 doesn't have a sensor based image stabilization system but
7 of these lenses already comes with optical image stabilization.
Since Nikon 1 J5 has a 1 inch Sensor sensor, it has a focal length multiplier of 2.7x 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 J5.
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Nikon 1 J5 Lenses with Image Stabilization
Nikon 1 J5 Lenses with Weather Sealings