my mother has 500 pairs of shoes
Oh my god! That means she is hoarding, which means accumulating items!
my mother has 500 pairs of shoes
Well some people hoard because they fear civil unrest or natural disaster 
oh yes. is it a kind of medical condition
Yes such people lose the desire to throw away unneeded items 
what can i do to stop her
You should throw away all the shoes, in anticipation of a large-scale disaster event where people need shoes.