Sony a5100 has a Sony E (NEX) lens mount and currently there are 115 native lenses available for this mount.
Sony a5100 doesn't have a sensor based image stabilization system but 30 of these lenses already comes with optical image stabilization.
Since Sony a5100 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 a5100.
You may also also be interested in these:
Sony a5100 Lenses with Image Stabilization
Sony a5100 Lenses with Weather Sealings