The task is to find the equation of the line that passes through the points $(-3, -5)$ and $(2, -2)$, and express the equation in the form $ax + by = c$, where $a$, $b$, and $c$ are integers in their lowest terms.

Step 1: Find the slope of the line

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(-3, -5)$ and $(2, -2)$ into the formula:

$m = \frac{-2 - (-5)}{2 - (-3)} = \frac{-2 + 5}{2 + 3} = \frac{3}{5}$

Step 2: Use the point-slope form to find the