South would be straight down (leg 1 of the triangle) and east would be right from that point (leg 2 of the triangle). Therefore, we are looking for the hypotenuse of the triangle.
Pythagorean Theorem: a^2 + b^2 = c^2
6^2 + 5^2 = c^2
36 + 25 = c^2
61 = c^2
c = sqrt(61)
c = 7.8 miles
Hope this helps!