Sony a5000 has a Sony E lens mount and currently there are 363 native lenses available for this mount.
The latest released lenses that are compatible with the a5000 are the Tamron 12-20mm f2.8, the Viltrox 26mm f2.8 FE and the SG-image AF 35mm f2.2.
Sony a5000 doesn't have a sensor based image stabilization system but
54 of these lenses already comes with optical image stabilization.
Since Sony a5000 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 a5000.
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Sony a5000 Lenses with Image Stabilization
Sony a5000 Lenses with Weather Sealings