Answer
$\frac{\pi}{10},\frac{\pi}{2},\frac{9\pi}{10},\frac{13\pi}{10},\frac{17\pi}{10} $
Work Step by Step
Step 1. Using the Addition Formula for the left side, the equation becomes $sin(3x+2x)=1$ or $sin(5x)=1$ which gives $5x=2k\pi+\frac{\pi}{2}$ and $x=\frac{2k\pi}{5}+\frac{\pi}{10}$ where $k$ is an integer.
Step 2. We can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{10},\frac{\pi}{2},\frac{9\pi}{10},\frac{13\pi}{10},\frac{17\pi}{10} $
