From what I've read, you cannot increase the shutter speed above 1/200's when using flash. Is this correct? I just want to make sure. Thanks!!
Yes, that is correct. Your D5100 only has X Sync with flash.
The D90 and up have a featured called Auto FP Sync for using faster than the fastest X Sync shutter speeds with Nikon hot shoe flash units that support Auto FP sync. Auto FP Sync does not work with any Nikon built-in flash
It really helps if you under stand how the camera works.
The shutter has 2 curtains. Nikon calls then the front and rear custains.
The front curtain opens so the image sensor can 'see' the image the lens is projecting. The shutter speed set determines how long the snsor gets to see-the-light- before the rear shutter curtain closes and stops the exposure.
The X-Sync speed is the fastest shutter speed where both shutter curtains are open. At 1/250 on your D5100 the rear curtain starts closing before the first shutter curtain is fully open, and both shutter curtains block a small postion of the image sensor from seeing-the-light.
One of the settings on your camera determines if a flash fires at the instant the front shutter curtain is fully open, or a the instant the rear shutter curtain starts to close. Each captures a different motion stopping effect if there is sufficient ambient light to be recorded in the scene. (see page 52 of the D5100 user's manual)
When using flash, shutter speed is no longer needed to stop motion. The duration of the flash of light is shorter than the X-Sync speed of the camera, 1/200. Your D5100 pop-up flash at full power likely has a duration of about 1/900 of a second. As the pop up flash power level is turned down the duration of the flash gets even shorter.