1. **State the problem:** Find the slope of the line passing through the points $(-3, -2)$ and $(1, 3)$.\n\n2. **Formula for slope:** The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. **Substitute the given points:** Here, $x_1 = -3$, $y_1 = -2$, $x_2 = 1$, and $y_2 = 3$. So,\n$$m = \frac{3 - (-2)}{1 - (-3)}$$\n\n4. **Simplify the numerator and denominator:**\n$$m = \frac{3 + 2}{1 + 3}$$\n$$m = \frac{5}{4}$$\n\n5. **Final answer:** The slope of the line is $\boxed{\frac{5}{4}}$.