Those colored dots are most likely image noise/hot pixels, not stars. In your example, ISO 3200 is very high, and that can make random red, green, and blue specks much more visible—especially in dark areas like the night sky.

For moon photos, try lowering the ISO and using a longer exposure instead of such a high ISO with a very fast shutter speed. That should reduce the colored speckling. If you’re doing longer night-sky exposures, the D5000’s noise-reduction options may also help, especially long-exposure noise reduction.

In general, these dots come from sensor noise and the camera’s color interpolation, where individual sensor pixels and their neighbors are used to build the final color image. In very dark areas, that can show up as isolated colored pixels.

To reduce it:

• lower ISO
• use a longer exposure where practical
• enable the camera’s noise-reduction features for long exposures
• if needed, use a faster lens so you don’t have to push ISO as high

So: they’re almost certainly not stars, but sensor noise made visible by your settings.