Let the starting point be at the origin with coordinates (0, 0).
The boy travels 5 km towards the South.
Position: (0, -5)
He turns left (which means he now faces East) and travels 5 km.
Position: (0 + 5, -5)
Position: (5, -5)
He turns to his right (which means he now faces South) and walks 7 km.
Position: (5, -5 - 7)
Position: (5, -12)
The distance from the starting point (0, 0) to the final position (5, -12) is:
d=(5−0)2+(−12−0)2
d=25+144
d=169
d=13
Therefore, the boy is 13 km from the starting point.