Random

Let the starting point be the origin $O(0,0)$ . North-south direction the $y$ -axis and east-west, $x$ -axis. He walks south for $7$ km to $A(0,-7)$ , then turns left (east) for $2$ km to $B(2,-7)$ , turns left (north) for $12$ km to $C(2,5)$ , and turns left (west) to $D(0,5)$ . Starting point $O$ is $\boxed{5}$ km south of $D$ .

In a cartesian, let's say his start point is (0, 7), then he walk down7, (0, 0). He walk to left 2,it become (2, 0), then he walk 12 upward, become (2, 12). Finally, he walk 2 to left become (0, 12).

Let's compare, (0, 12) and (0, 7) the different between them is 5 km. That's the answer.