Explanation

(c)
$\cos^{- 1}{\left( \cos\frac{5\pi}{3} \right) + \sin^{- 1}\left( \cos\frac{5\pi}{3} \right)}$
$\ \ \ \ \ = \cos^{- 1}{\left( \cos\frac{5\pi}{3} \right) + \sin^{- 1}\left\lbrack \sin\left( \frac{\pi}{2} - \frac{5\pi}{3} \right) \right\rbrack}$
$\ \ \ \ = \frac{5\pi}{3} + \frac{\pi}{2} - \frac{5\pi}{3} = \frac{\pi}{2}$
Alternate
Since, $\cos^{- 1}{x + \sin^{- 1}{x = \frac{\pi}{2}}}$
$\therefore\ \cos^{- 1}{\left( \cos\frac{5\pi}{3} \right) + \sin^{- 1}{\left( \sin\frac{5\pi}{3} \right) = \frac{\pi}{2}}}$