5. The maximum value of the function $y=\sqrt{1}+\sin x+\sqrt{1-\sin x}$ is ().
(A) 2.
(B) $\sqrt{5}$.
(C) $\sqrt{6}$.
(D) $\sqrt{2}$.
(E) None of the above.
$$
\text { 5. Since } \begin{aligned}
y^{2} & =\left(\sqrt{1+\sin x}-\sqrt{1-\sin x)^{2}}\right. \\
& =2-2 \sqrt{(1+\sin x)(1-\sin x)} \\
& =2-2|\cos x|,
\end{aligned}
$$
if $|\cos x| \leqslant 1$,
therefore, when $x=k \pi$ ( $k$ is an integer), $y$ reaches its maximum value of 2. Hence, the correct choice is (A).
$$