A line parallel to the x-axis is horizontal and thus any point on the line has a fixed y-coordinate. So the given line that passes through (-5, 4) has equation y = 4 with slope 0.
A line perpendicular to this one would be vertical. Its slope would be undefined (or infinite, depending on convention), so that any point on it has a fixed x-coordinate. If this line also passes through (-5, 4), then its equation would be x = -5.