Nikon AF-S DX VR Zoom-Nikkor 55-200 mm f/4-5.6G IF-ED Lens?

Am using Nikon d5100… Can i use this lens for macro photography?

No.

It's a telephoto lens. These lenses are good at magnifying things that are far away, but not good at magnifying things that are small.
The reason is the close focus limit - you can't get very close to your subject with this lens; it loses the ability to focus several feet from the lens.

For macro photography you need a macro lens, such as the Micro Nikkor 60mm f/2.8 AF-S.
Alternatively you can use the 50mm/1.8D and extension tubes. This is far cheaper ($140 in total), but you will have to focus and meter manually. Focusing manually is recommended for macro photography anyway, but the loss of automatic metering might bother you. Some more expensive extension tubes support metering, but they are that much more expensive that you can just buy the 60mm macro lens then.

Note that if you want to go the cheap extension tube route, then having a lens with aperture ring is necessary, such as the aforementioned 50mm f/1.8D AF. The 50mm/1.8G AF-S does not have an aperture ring. The version with aperture ring won't autofocus at all on your camera though…

No. It will get you a bit closer but not anything like proper macro. The cheapest proper macro lens for Nikon is Nikon's own 40mm FX AF-S f2.8 micro, which is not much more expensive than the 55-200mm zoom. (Nikon call macro lenses micro for some unknown reason).

The 40mm lens isn't bad, but it does have a problem with being so short in that you have to get very close to the subject. That isn't always convenient and even when it is, you will tend to block the light with your body or camera getting in the way.

The next cheapest lens is the 60mm f2.8 Micro lens, which is actually a very nice lens, although it is about twice the price of the 40mm one. Be careful though - your D5100 will only autofocus with the AF-S version of the lens. The cheaper AF-D version is older and won't autofocus with a D5100. Arguably you shouldn't use autofocus with macro anyway, but you don't have to use it as a macro lens all the time, so AF is worth having.

Next up is the 85mm ED VR G AF-S f3.5 Micro lens. My wife has one. It is light and works great with a D5100.It's not much more expensive than the 60mm lens but the VR is useful when you aren't using it as a macro lens. At 1:1 macro, VR makes just about zero difference! The 85mm lens lets you use AF and then override it by turning the end of the lens barrel. Best of both worlds.

Beyond that the lenses start getting very expensive. The longer Nikon Micro lenses are fantastic quality, but you do need a large wallet!

An alternative is extension tubes. If you decide to go for those instead, don't go for the cheap ones. They won't pass through the aperture information properly. Get some which have the circuitry to maintain auto focus and TTL auto exposure, like these:
http://www.amazon.co.uk/...002YIY44O/

I took a series of macro photos over the weekend. I used a D5100, elcheapo extension tubes (like <$20) and a $40 ebay 50mm f1.8E lens. The lens is an old manual lens with an f ring, meaning I have to use the M mode and adjust the aperture and shutter speed manually. I've also used a $20 ebay Vivitar 28mm lens with Nikon mount, it works fine as well. The extension tubes have three sections and a front and rear section with Nikon mounts. I have photos of dew drops refracting the sky and grass blades, one drop that acts as a magnifying lens and enlarges the tiny jagged edges of the leaf blade. I also have macros of dandelion pistals with individual grains of pollen on them.

Yes, a $250-$500 Nikon macro lens would be great, but you can have just as much fun with $40-$60 worth of ebay tube and lens. If you then really feel the need for an expensive macro lens, you can go for it. Just don't get stuck on the lens f stop. With anything less than f5.6, the depth of field is so narrow on ultra close ups that you can have a tiny drop of water or spider web in the middle of a grass leaf be in focus, but the leaf edge ahead and behind the drop or web be blurry.