To determine the equation of a line that is perpendicular to the line $y = 1$ and passes through the point $(-5, 1)$, begin by recognizing the orientation of the given line. The equation $y = 1$ describes a horizontal line. Any line that is perpendicular to a horizontal line must be a vertical line, which is expressed in the general form $x = a$. Because this particular vertical line must contain the given point $(-5, 1)$, its $x$-coordinate is held constant at $-5$. Thus, the equation of the line is precisely $x = -5$.