16sin^5(x)-20sin^3(x)+5sin(x)

$16sin^5x-20sin^3x+5sinx=0$
$5sinx-20*( \frac{3sinx-sin3x}{4} )+16sin^5x=0$

$5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4} )+16sin^5x=0$

$5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4} )+16*( \frac{10sinx-5sin3x+sin5x}{16} )=0$

$5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4})+16*(\frac{5sinx}{8}-\frac{5sin3x}{16}+\frac{sin5x}{16})=0$

$5sinx+(5sin3x-15sinx)+16*(\frac{5sinx}{8}-\frac{5sin3x}{16}+\frac{sin5x}{16})=0$

$5sinx-15sinx+5sin3x+(10sinx-5sin3x+sin5x)=0$

$sin5x=0$

$5x= \pi n$ ; n∈Z
$x= \frac{ \pi n}{5}$ ; n∈Z