Answer
$258.69^\circ.$
Work Step by Step
If $v=ai+bj$ then by definition $tan(\alpha)=\frac{b}{a}$, hence $\alpha=tan^{-1}(\frac{b}{a})$. Also $0^\circ\lt\alpha\lt360^\circ.$
Therefore here $\alpha=tan^{-1}(\frac{-5}{-1})=tan^{-1}(5)=78.69^\circ+180^\circ=258.69^\circ.$ (because it must be in Quadrant III).