Welcome to Nikonians! My daughter is a competitive cheerleader so I shoot a lot of cheerleading. What exposure mode are you using?
I assume they are performing in a gym. Many are lit like dungeons so getting enough light is always a problem.
Could you be more specific as to what is wrong with your images? (blurry?)
Since your subject is moving you will have to use a fast shutter speed to freeze their motion. Set the shutter speed to 1/250th sec. minimum or faster if at all possible.
You will have to turn the ISO up (ISO 800-3200 or even HI (ISO 6400) may be required.) depending on the ambient light level.
Now, regarding your lens; Your lens is very capable of capturing fast moving subjects in good lighting (sunlight). When shooting sports in low light (gyms, etc...) a fast lens is the price of entry. Fast Constant aperture f/2.8 lenses in the 70-200mm range start at about $700.00 and go up to $2400.00.
To get the most light possible through the 55-200mm you will have to shoot at the 55mm zoom setting (f/4) which will provide a full stop more light than shooting at 200mm (f/5.6). A one stop difference is the equivalent of doubling the light. In other words you can use a shutter speed twice as fast at 55mm (f/4) than you can at 200mm (f/5.6). f/2.8 is one stop faster than f/4 and two stops faster than f/5.6.
I use (f/2.8) constant aperture zooms and even faster primes. My settings are as follows: Shutter Speed: 1/250th - 1/500th sec. Aperture (f-stop): f/2.8 ISO: 800 to 6400 depending on ambient lighting conditions.
If you keep the zoom set at 55mm (f/4)on your lens you will only have to gain one stop of ISO over what I would be shooting at. In dark gyms you will have issues with noise but at least you will be able to capture an image.
I always shoot in Manual exposure mode, however if you use Shutter Priority (S) mode with the Shutter Speed set at 1/250th sec. and Auto ISO setting the maximum sensitivity to ISO 3200 or HI (ISO 6400) if required. (see page 149 of the D5000 Users Manual.)
The alternative is to use Aperture Priority (A) mode and watch the shutter speed in the viewfinder then adjust the ISO accordingly. Good Luck and Enjoy your Nikons!