Answer
$\sin \theta= \frac{12}{13}$, $\tan \theta=\frac{12}{5}$.
Work Step by Step
$\cos^{2}\theta+\sin^{2}\theta=1$
$\implies \sin^{2}\theta= 1-\cos^{2}\theta=1-\frac{25}{169}=\frac{144}{169}$
$\implies \sin \theta= \frac{12}{13}$ ($\sin \theta$ is positive as $0\leq\theta\lt\frac{\pi}{2}$)
$\tan \theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$.
