Answer
$258.69^{\circ}$
Work Step by Step
Let us consider that a vector $v$ is given by $v=pi+qj$ and makes an angle of $\alpha$ with the positive $x$-axis. The direction angle $\alpha$ for the given vector can be determined using the formula:
$\tan \alpha=\dfrac{q}{p}$
Here, we have: $v=-i - 5j $
Now, $\tan \alpha=\dfrac{ -5}{-1}=5$
Since the angle must be in the quadrant III, the direction angle is: $\alpha=\arctan (5) \approx 78.69^{\circ}+180^{\circ}=258.69^{\circ}$
