I attached a flash on to my d5300, but shutter speed is not limited to 1/200. Why ?

It is normal for that case.

Not sure what you mean by "beyond 1/200 sec."  Do you mean your shutter speed can be 1/500 sec or 1/1000 sec when the flash is attached. If so, then there is something wrong. Camera makers design a camera to only fire a shutter at X-sync speed only because that is the speed when the shutter curtain is fully open. In other cameras with slower shutter curtains, the shutter speed is often limited to 1/125, 1/90 or even 1/60 sec. My first SLR camera, bought in 1979, only allowed me to use a flash when the shutter speed is set to 1/60 or slower because it has a horizontally traveling cloth curtain. Modern cameras have faster shutter curtains, usually metal and vertically travelling, and so the X sync speed can be as fast as 1/200 sec. or even faster

Of course most cameras also allow the shutter speed to be slower than the x sync speed when using flash. That means for your camera, you can set the camera so that it will still fire with the flash at 1/125 sec., 1/60 sec., 1/30 sec. etc. If that is what you mean by "beyond 1/200 sec." then nothing is wrong. You can even turn off the option to use slower shutter speeds in your camera's menu system if you want Also, while the flash is charging (not ready to fire ), the flash will allow the camera to set any shutter speed, but once the flash is fully charged, then it will set the shutter speed to 1/200 sec. or it will allow a slower shutter speed than that if that is how you configured your camera. Lastly, if the flash you use is not compatible with Nikon cameras then the flash will not set the shutter speed on your camera. In that case, you yourself will have the set the camera's shutter speed yourself 

The flash may not be fully TTL-compatible to your camera or the camera is in manual mode. The flash may fire but the camera will shoot according to the settings in place. Only a part of the photo will come out illuminated by the flash or none at all.

It could be that your camera doesn't recognize that the flash is attached.  This could be a broken flash, but it's more than likely that the flash is not pushed forward onto the shoe and thus its contacts are not touching those of the camera.

DSLRs use focal plane shutters that are comprised of two linear-motion curtains. From zero to 1/200 seconds shutter speed on your camera, the film (image sensor) is unobstructed by the curtains. At faster shutter speeds, the shutter curtains always cover some percentage of the film plane. Thus, if you use a flash above the x-sync rate (1/200 sec for the D5300 and many Nikon DSLRs) only a fraction of the film plane will be exposed when the flash goes off. High-speed sync flash solves this problem by sending out multiple flashes which ensures that the film plane is fully illuminated by the flash.

Perhaps the following links of how a FPS works will clear things up.

https://www.youtube.com/watch?v=KS4sXkPNJs8

https://en.wikipedia.org/wiki/Focal-plane_shutter