The total angle turned through after each of the first 4 moves is 10^°, 30^°, 60^° and 100^°. So the robot does not face due East at the end of a move in its first complete revolution. The total angle it has turned through after each of the next 5 moves is 150^°, 210^°, 280^°, 360^° and 450^°, so at the end of the 9th move the robot does face due East. As the robot moves 5m in each move, the distance it travels is 45m.

Note that this solution assumes that the robot is not starting the process close to the North Pole!