2. ** Given the function $y=\sin x+a \cos x$ is symmetric about the line $x=\frac{5 \pi}{3}$. Then the function $y=a \sin x+\cos x$ is symmetric about the line ( ) .
(A) $x=\frac{\pi}{3}$
(B) $x=\frac{2 \pi}{3}$
(C) $x=\frac{11 \pi}{6}$
(D) $x=\pi$
Let $f(x)=\sin x+a \cos x, g(x)=a \sin x+\cos x$. According to the problem, we have $f(x)=$ $f\left(\frac{10 \pi}{3}-x\right)$.

Also, $f(x)=g\left(\frac{\pi}{2}-x\right)$, so $f\left(\frac{10 \pi}{3}-x\right)=g\left(\frac{\pi}{2}-\frac{10 \pi}{3}+x\right)$, thus $g\left(\frac{\pi}{2}-x\right)=g\left(\frac{\pi}{2}-\frac{10 \pi}{3}+x\right)$. Therefore, one axis of symmetry for $g(x)$ is
$$
x=\frac{1}{2}\left(\frac{\pi}{2}+\frac{\pi}{2}-\frac{4 \pi}{3}\right)=-\frac{\pi}{6} .
$$

Since the period of $g(x)$ is $2 \pi$, another axis of symmetry is $x=-\frac{\pi}{6}+2 \pi=\frac{11 \pi}{6}$. Therefore, the answer is C.