To write the equation of a line that is perpendicular to the line $y = -5$ and contains the point $(-4, -5)$, first evaluate the geometry of the given equation. The equation $y = -5$ represents a horizontal line. Since perpendicular lines intersect at a right angle, a line perpendicular to a horizontal line is a vertical line, denoted by the form $x = a$. Given that the required line passes exactly through the coordinate $(-4, -5)$, every point on this line shares the constant $x$-coordinate of $-4$. Therefore, the definitive equation of the perpendicular line is simply $x = -4$.