A line that is perpendicular to the y-axis is a vertical line. Vertical lines have equations of the form \( x = k \), where \( k \) is a constant.
Since we want the line to pass through the point \( (5, -2) \), the equation of the line will be:
\[ x = 5 \]
So, the equation of the line that is perpendicular to the y-axis and passes through the point \( (5, -2) \) is \( x = 5 \).