1. **State the problem:** Find the equation of the line passing through the points $(-6,5)$ and $(-3,-3)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}.$$\n\n3. **Calculate the slope:** Substitute the points: $$m=\frac{-3 - 5}{-3 - (-6)}=\frac{-8}{-3 + 6}=\frac{-8}{3}.$$\n\n4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1).$$ Using point $(-6,5)$, we get $$y - 5 = -\frac{8}{3}(x + 6).$$\n\n5. **Simplify the equation:** Distribute the slope: $$y - 5 = -\frac{8}{3}x - \frac{8}{3} \times 6 = -\frac{8}{3}x - 16.$$\n\n6. **Isolate $y$:** $$y = -\frac{8}{3}x - 16 + 5 = -\frac{8}{3}x - 11.$$\n\n7. **Final answer:** The equation of the line is $$y = -\frac{8}{3}x - 11.$$