This "road" they are running is basically an L-shape, and combined with the direct distance from start to end forms a triangle. This triangle has a hypotenuse of 13 (since the direction of the road changes from south to west, we can pretty much assume that it is a right triangle with legs of 5 and X.)
So to find X, we use the Pythagorean Theorem.
a²+b²=c²
(5)²+X²=13²
25+X²=169
X²=144
Distance cannot be negative, so we know that X=12. This is the length of the remainder of the road.
To find total distance, just add the two lengths of road together.
5+12=17
