I have recently started DSLR photography, and love taking long exposures of the night sky.
I would like to have the sky be black, instead of blue, seen here: https://flic.kr/p/xRVXcw
I have a Nikon D5000, and would like to know what settings I should use for a black sky.
As WayneF commented in your question, it looks like you took the picture too early in the evening. The EXIF data indicates you took it at 8:49 PM DST in late August. You are probably in the period called astronomical twilight, defined as when the sun is between 12˚ and 18˚ below the horizon. Wait a bit longer, and the sky should be as dark as it's going to get for your location.
If the moon is in the sky, even a sliver, there will be enough light to turn the sky blue. The sky is blue due to a phenomenon called Rayleigh scattering, which is the diffuse scattering of sunlight. The light from the moon is just reflected sunlight, albeit about a million times weaker in intensity (or about 18-20 stops in photographic terms). Based on the EXIF date and time of your photo, the moon could have been up for as much as 3 hours in, say, New England, for example. In fact, the 27th of August was 2 days before the full moon, and it was about 96% of fully illuminated.
But without even consulting moon tables/calculators, you can tell there is some significant diffuse light in your photo because of the general daylight-like quality of lighting and highlights in the trees.
Note that depending on exactly where you are shooting, there might be too much light pollution to ever get a truly "dark sky".
There are several resources to find your location's sunset/sunrise, moonset/moonrise, and civil/nautical/astronomical twilight times, such as timeanddate.com on the web, The Photographer's Ephemeris for mobile and desktop apps, to name a couple.
In addition to the excellent answer by @scottbb:
It also appears that the ambient light falling on the trees may be from a very warm source, such as tungsten lights or sodium vapor lights, and that will skew the Auto White Balance in the cooler/blue direction to compensate.
When photographing the night sky it is best to shoot raw, so you can modify and fine tune white balance however you want in post processing. But a good starting point is to set the in-camera WB to 5200K and avoid shooting in areas where artificial lights that are usually very warm in terms of color temperature have an influence on foreground objects and even the sky as some of their light will reflect off dust and moisture in the air.
So why 5200K? Because you are photographing stars. And stars are just suns more distant than our own. We usually see our own Sun as neutral in color. The light from our Sun, when filtered by the Earth's atmosphere is centered at around 5200K.
