If $f(x)=2 \tan^{-1} x + \sin^{-1} \bigg(\large\frac{2x}{1+x^2}\bigg),$$x >1$ then $f(5)$ is equal to

Question

$\begin{array}{1 1} \frac{\pi}{2} \\ \pi \\ 4 \tan^{-1}(5) \\ \tan^{-1} \bigg(\frac{65}{156} \bigg) \end{array}$