Answer
Carlos ends up 1268 meters north of his starting position.
Work Step by Step
We can find the total displacement that Carlos runs in ten minutes;
$d = v~t = (5.0~m/s)(600~s) = 3000~m$
We can find the north component of Carlos' displacement vector;
$d_{north} = (3000~m)~sin(25^{\circ})$
$d_{north} = 1268~m$
Carlos ends up 1268 meters north of his starting position.
