If $x>0$ and $\sin^{-1}\bigg(\large{\frac{5}{x}}\bigg)+\sin^{-1}\bigg(\frac{12}{x}\bigg)=\large\frac{\pi}{2},$ than find the value of $x$.

Question

$\begin{array}{1 1} \pm 13 \\ \pm \frac{1}{13} \\ \pm \frac{5}{12} \\ \pm \frac{12}{5} \end{array} $