Using Pythagoras’ Theorem, x²+y²=64 so y²=64-x² where x is horizontal distance and y the vertical distance.
Differentiating wrt time, t: 2ydy/dt=-2xdx/dt or ydy/dt=-xdx/dt. This means that if the foot of the ladder moves away from the wall, the top of the ladder slides down the wall. As x increases, y decreases.
y=√(64-x²), so dy/dt=-(xdx/dt)/√(64-x²).
We now substitute x=5 to find the instantaneous value of dy/dt=-5(2)/√39=-1.60 ft/s, that is, 1.60 ft/s downwards (approx).