Let $S$ be the set of points $z$ in the complex plane such that $|z - 7 + 10i| \le 5.$  Find the area of $S.$
I recognize that the inequality $|z - 7 + 10i| \le 5$ describes all the points that are at most 5 units away from the point $7 - 10i$ in the complex plane. This means that $S$ is a circular region with center $7 - 10i$ and radius 5. To find the area of $S,$ I just need to apply the formula for the area of a circle, which is $\pi r^2.$ In this case, $r = 5,$ so the area of $S$ is $\pi (5^2) = 25 \pi.$ 