1. **State the problem:** Find the slope of the line passing through the points $(-5, 3)$ and $(5, -3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the points:** Here, $x_1 = -5$, $y_1 = 3$, $x_2 = 5$, and $y_2 = -3$. So, $$m = \frac{-3 - 3}{5 - (-5)} = \frac{-6}{5 + 5} = \frac{-6}{10}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{-6}}{\cancel{10}} = \frac{-3}{5}$$ 5. **Interpretation:** The slope is negative, indicating the line goes downwards from left to right. **Final answer:** The slope is $-\frac{3}{5}$.