To simplify this expression, we first need to break down each term:

5^{13} = 5 5 5 5 5 5 5 5 5 5 5 5 5 = 1220703125
125^{2} = 125 125 = 15625
25^{9} = 25 25 25 25 25 25 25 25 * 25 = 1953125

Now we can substitute these values back into the expression:

1220703125 * 15625 / 1953125

Now we can simplify by canceling out any common factors:

= 7812500000 / 1953125
= 4000

Therefore, 5^{13} * 125^{2} / 25^{9} equals 4000.