$n=10$
$(\large\frac{10}{2}$$+1)^{th}=6^{th}$ term
$T_6=10C_5.\large\frac{1}{x^5}.$$x^5 \sin ^5x$
$10C_5=\large\frac{10!}{5!5!}=\frac{10\times 9\times 8\times 7\times 6\times 5!}{5\times 4\times 3\times 2\times 5!}$
$\Rightarrow 252$
$252 \sin ^5 x=\large\frac{63}{8}$
$\Rightarrow \sin ^5 x=\large\frac{1}{8}$
$\Rightarrow \sin ^5 x=\large\frac{1}{2^5}$
$\Rightarrow \sin x=\large\frac{1}{2}$
$\Rightarrow x=n\pi +(-1)^n \large\frac{\pi}{6}$
Hence (C) is the correct answer.