Could someone verify my answer for this question?

13m ladder is leaning against a wall.

If the top of the ladder slips down the wall at a rate of 2m/s.

How fast will the foot be moving away from the wall when the top is 5m from the ground?

My answer:

use pythagoras to set up equation x^2 + y^2 = 13^2

Then I differentiate this implicitly and get the equation 2x dx/dt + 2y dy/t = 0

Then I fill in the values and get 5/6 m/s.

Is this correct?