Is this lens good for wildlife and sports? Im getting a nikon D5100 And my brother plays soccer and I'm in gymnastics. I love taking pics of sports. Is this lens good enough?
I'd say "no, it's not good enough", but it's hard to rule it out absolutely without knowing more details about you're going to try using it. To take each of your three use cases:
- Wildlife: probably not enough reach. You're looking at 400mm or more for typical wildlife photography.
- Football: If you can get somewhere near the sidelines, 200mm probably gives you enough reach to cover the near half of the field. f/5.6 will be fine for daytime sports, but won't be useful under lights.
- Gymnastics: too slow. It depends a lot on your gym and how close you can get to the action, but if you're at f/5.6 then you're probably going to be around ISO 6400 to freeze the action - and that's marginal at best on a crop sensor.
Stepping back a bit, there are two significantly different categories of photography you're trying to cover here: wildlife and (daytime) outdoor sports, which require a long focal length but not necessarily that fast a lens, and indoor sports, which don't require such a long focal length, but do need a fast lens. Don't expect to be able to manage both of those with just one lens.
For sports photography, you need to be able to use a fast shutter speed as you'll always want to use 1/500s or faster exposures in order to avoid motion blur (rule of thumb, 1/250s or faster for posed photos, 1/500s or faster for people moving). A wider aperture would therefore be recommended. I wouldn't say that a f/5.6 would be enough, except in bright outdoor daylight.
For indoor sports, or sports at night/dusk, you especially need a very fast lens in order to have the best chance of capturing sharp images. This is why people buy fixed f/2.8 zooms or f/2.0 teles that look like they weigh as much as a motorbike.
For wildlife photography if you're shooting during bright outdoor daylight, you can get away with a little narrower aperture in a pinch provided you have the reach (which you may not at only 200mm), but you'd still want wider aperture to be more versatile in your lighting conditions.
So in all three of these scenarios, f/5.6 (at the tele end, because you don't photograph sports or wildlife only at the widest end of your zoom) is not enough.
A prime telephoto lens is going to allow you to get a wider aperture for much less money but result in the inability to zoom out. So you'd need to have a certain reach in mind or be prepared to swap lenses according to the situation.
I'm in gymnastics
The widest aperture on the Nikon 55-200 f/4-5.6 is pretty slow, so you'll have trouble at indoor sporting events. Even outdoors, it'll be pushing your camera's ISO above 400, probably. It'll get the job done, but "good enough" is a very vague term; you will be compromising ISO or shutter speed to varying degree with this lens, but you get what you pay for.