1. **State the problem:** We need to determine the period of a sinusoidal graph given its maximum and minimum points. 2. **Identify key points:** The graph has maxima at $(-3\pi, 5)$ and $(\pi, 5)$, and minima at $(-5\pi, -1)$, $(-\pi, -1)$, and $(3\pi, -1)$. 3. **Recall the period formula:** The period $T$ of a sinusoidal function is the horizontal distance between two consecutive maxima or minima. 4. **Calculate the period:** The distance between the maxima at $-3\pi$ and $\pi$ is $$T = \pi - (-3\pi) = \pi + 3\pi = 4\pi$$ 5. **Verify with minima:** The distance between minima at $-5\pi$ and $-\pi$ is $$-\pi - (-5\pi) = -\pi + 5\pi = 4\pi$$ This confirms the period is consistent. 6. **Final answer:** The period of the sinusoidal graph is $$\boxed{4\pi}$$