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 $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the points:** $$m = \frac{3 - (-3)}{5 - (-5)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{3 + 3}{5 + 5}$$ 5. **Calculate the values:** $$m = \frac{6}{10}$$ 6. **Simplify the fraction by dividing numerator and denominator by 2:** $$m = \frac{\cancel{6}^3}{\cancel{10}^5} = \frac{3}{5}$$ 7. **Interpretation:** The slope of the line is $\frac{3}{5}$, which means for every 5 units moved horizontally, the line rises 3 units vertically. **Final answer:** The slope of the line is $\boxed{\frac{3}{5}}$.