5. (2004 National College Entrance Examination - Tianjin Paper) The interval of the function $y=2 \sin \left(\frac{\pi}{6}-2 x\right)(x \in[0, \pi]$ where it is monotonically increasing is
A. $\left[0, \frac{\pi}{3}\right]$
B. $\left[\frac{\pi}{12}, \frac{5 \pi}{12}\right]$
C. $\left[\frac{\pi}{3}, \frac{5 \pi}{6}\right]$
D. $\left[\frac{5 \pi}{6}, \pi\right]$
5. C $y=-2 \sin \left(2 x-\frac{\pi}{6}\right)(x \in[0, \pi])$, which means to find the decreasing interval of $y=2 \sin \left(2 x-\frac{\pi}{6}\right)(x \in[0, \pi])$.