What wide-angle lenses work well on a Nikon D5000 for night and landscape photography?

Your D5000 uses the Nikon F mount, so many Nikon F-mount lenses will fit. The main limitation is autofocus: on the D5000, lenses with their own AF motor will autofocus; older lenses without one will require manual focus, and some older lenses may also limit metering/aperture communication.

For night photography, a fast lens is usually the best choice, since you want as much light as possible. Good options mentioned were the Tokina 11-20mm f/2.8 (or older 11-16mm f/2.8) if you want an ultra-wide zoom, and the Nikon 20mm f/1.8 if you want a very bright wide prime. A constant f/2.8 wide zoom can also be a versatile landscape option.

Your ND filter won’t help for night shooting because it reduces light. In general, filters are not especially useful for night photography. For landscapes, filters can be situational, but for night work the lens speed matters much more than filters.