\(sin3x\in\left[-1;1\right]\Rightarrow y=5sin3x-1\in\left[-6;4\right]\)
\(\Rightarrow y_{min}=-6\Leftrightarrow sin3x=-1\Leftrightarrow x=-\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\)
\(y_{max}=4\Leftrightarrow sin3x=1\Leftrightarrow x=\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\)