You can very well take night shots like this with D5100. I'll explain from my experience when i took this pic.

Time

Timing is very important in city-light shots. You can see the deep-blue/purple color of sky in the example picture you posted. You get this color a bit after sunset (Twilight). Unlike other landscape shots, you need a clear sky. So plan your trip to the observatory accordingly.

Lens

A wide angle lens is the most suitable for city-light shots. Apart from getting a wide viewing angle you also get a good depth of field.

Aperture

What you need is a large depth of field. Setting it more than f/8 on a wide angle lens gives you good depth of field. Few city-light shots look particularly good if you go all the way to f/22. You get star burst from light. But this depends on your lens.

Shutter speed

I exposed my light meter off the blue sky. It gave me some 10s of shutter speed. Generally it is a good idea to meter off the blue sky.

Tripod

You definitely need a tripod or a solid support for your camera. Exposure time is going to be much more than you can hand hold the camera.

Other consideration

1. Observatories have big glass windows. And at night they start reflecting room lighting. Be ready to post-process them out.
2. Shoot raw. You might want to change WB later.
3. Use lens hood.

About the actual image

1. Looks like the photographer has set a cooler WB on the image. I reduced WB of my image to get this look:

   

2. The EXIF data of image shows it is shot at 1/30th of second. To compensate this faster shutter speed aperture is increased to f/2.8 and ISO bumped up to 1250. The reason of using a fast shutter speed is not very clear to me. It could be because tripods might not be allowed (?) in John Hancock observatory, Boston.