Is this lense compatible with my nikon d5200?

Will it autofocus?

http://www.amazon.com/...00005Y3OM/

It is compatible, but will not auto-focus.

You need to be looking at all the Nikkor AF-S lenses for your fine D5200 camera

Because it is the cheapo version 70-300mm, besides not autofocusing its deficiencies are likely to be magnified by the 24 MP of the D5200.

No, but this one will: http://www.amazon.com/...000HJPK2C/

Only Nikon's more expensive AF-S lenses will auto focus on your D5200. You can use the lens you linked to on your D5200 but only with manual focus. Also, the lens you show doesn't have VR (Vibration Reduction) and its really needed on a zoom of this focal length.

The lens you need is the AF-S VR Zoom-Nikkor 70-300mm f4.5-5.6G IF-ED.

Yes but it won't auto focus on the D5200 because the D5200 doesn't have a built in AF motor. The lowest end Nikon DSLR to feature a built in AF motor would be the D7000.

The 55-300mm G ED Vr is a better option since it has a better focal range a metal mount and overall better build quality.

http://www.amazon.com/...003ZSHNCC/

Or if you wanted a better option then buy the 70-300mm VR. Its the heaviest of the three but it has the best optics.

http://www.amazon.com/...000HJPK2C/