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

Question

( A ) $\frac{\pi}{2}$
( B ) $\pi$
( C ) $4 \tan^{-1}(5)$
( D ) $\tan^{-1}(\frac{65}{156})$