Answer
$\cot\theta$ = $\frac{12}{5}$
Work Step by Step
Ratio identity for $\cot\theta$ is-
$\cot\theta$ = $\frac{\cos\theta}{\sin\theta}$
Substituting given values of $\sin\theta$ and $\cos\theta$-
$\cot\theta$ = $\frac{-\frac{12}{13}}{-\frac{5}{13}}$
= $\frac{12\times 13}{13\times5}$ = $\frac{12}{5}$
or $\cot\theta$ = $\frac{12}{5}$
