Any line that is perpendicular to a given line y = ax + b must have slope -1/a
For the lines -x - 5y = 7 and 5x - y = -9, first, we rewrite them in the slope-intercept form:
y = -x/5 - 7/5
y = 5x + 9
We can check that the slope of the first line is the negative inverse of the slope of the second line. Therefore, the lines are perpendicular.