Answer
The amplitude is $2$, the period is $\frac{2\pi}{5}$, there is no vertical translation and the phase shift is zero.
Work Step by Step
We first write the equation in the form $y=c+a \sin [b(x-d)]$. Therefore, $y=2\sin (5x)$ becomes $y=0-2\sin [5(x-0)]$
Comparing the two equations, $a=-2,b=5,c=0$ and $d=0$.
The amplitude is $|a|=|-2|=2.$
The period is $\frac{2\pi}{b}=\frac{2\pi}{5}=\frac{2\pi}{5}$.
The vertical translation is $c=0$.
The phase shift is $|d|=|0|=0$
Therefore, the amplitude is $2$, the period is $\frac{2\pi}{5}$, there is no vertical translation and the phase shift is zero.
