Nikon 50mm f/1.8 G on D5100 for indoor equine?

So i've been doing some research for a couple of hours on what lens is best for indoor equine.
Now my 55-200 f/4 well.yeah.that's no use!

Someone had quoted:
"I need f/1.8 for ISO 3200-6400 at 1/500 on my D5100. Indoor sports has to be the most expensive thing to photograph!"

The photo under neath of the horse indoor with poor light was fantastic, visible noise was there, but it didn't bother me the slightest.

***I don't want to be wasting my money on this lens if i do buy it, but as its "50mm" is it that only? So no zoom?***

There's the 85mm but that's not compatible with the d5100:'(

***And would it shoot better videos too? Or is that to do with the video quality (as some frames are completely blurred out then 1-2 frames are in focus***

Thanks! Lots of research going into this!

Added (1). The zoom isn't a massive thing to me as i will be right next to the action/moving around etc

The 50 mm is pretty short and is usually considered a portrait lens.

When I shoot equine events, I use a Nikkor AF-S 200-400 mm f/4 lens mounted on a monopod

New nikon af-s 85/1, 8G is fully compatibile with D5100