Need astrophotography

I really want to take some photos of planets and galaxys maybe but i'm not sure what equipment i need?

I have a nikon D5200 and a af-s nikkor 55-300mm 1:4.5-5.6GED lens but what other stuff would i need for my camera?

You need a T mount adapter and a telescope. This article may help you get started.
http://www.imaging-resource.com/ARTS/ASTRO/ASTRO.HTM

RetiredPhil is right.

A good telescope with an adapter for your D5200 would be a good start.

A 300 mm lens can hardly fill the screen with the moon.

Here is a sample of a shot of the moon, using a 500 mm lens and 2x teleconverter.

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This is NOT a good example of a moon shot, but placed on this website to show some of the issues that can cause less than perfect shots of the moon, planets or star groupings.

* A shot of the full moon will appear flat, since the lighting is the same as shooting here on earth in the middle of the day. The best time is to shoot when the moon is about in one quarter light, with the sidelight showing the textures of the moon's surface
* When shooting, even at high shutter speeds, there can be some unwanted blur caused by camera movement.

If you buy a telescope with a motor drive and controlled by a computer, long exposures of stars can be accomplished.

Just a note on cost.

* A fine computer controlled telescope with attachments for your D5200 costs less than $1,000.

* A 500 mm lens costs about $8,600 and the 2x teleconverter about $500.

Just save your pennies until you can buy for what you want

There are several methods you can try.

The 500 Rule. http://www.davidkinghamphotography.com/blog/2012/11/how-to-avoid-star-trails

Divide 500 by the focal length of the lens used. Then round the answer down and divide by the 1.5x crop factor of your camera. Round this answer down and that's your exposure time.

500/18 = 27.8. 27/1.5 = 18 so 18 seconds is your exposure time.

NOTE: I saw no mention of what aperture and ISO to use. Start at ISO 800 and f3.5. If your image is too light stop down 1 stop. If your image is too dark try ISO 1600.

http://www.fredmiranda.com/astrotrac/

http://astropix.com/HTML/I_ASTROP/TOC_AP.HTM

http://www.popphoto.com/how-to/2008/12/how-to-astrophotography-101

http://digital-photography-school.com/how-to-shoot-the-night-sky-introduction-to-astrophotography/