To simplify the expression:

4c^4d^8 / 20(c^2d^5)^2

First, simplify the expression inside the parentheses:
(c^2d^5)^2 = c^4d^10

Now substitute the simplified expression back into the original expression:
4c^4d^8 / 20(c^4d^10)

Next, simplify the constants:
4 / 20 = 1/5

Now simplify the variables:
c^4 / c^4 = 1
d^8 / d^10 = 1/d^2

Finally, put it all together:
(1/5) * (1/d^2) = 1/5d^2

Therefore, the simplified expression is 1/5d^2.