Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. $(-5,6) ; y=\frac{1}{5} x-5$

Write an equation for the perpendicular line in slope-intercept form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Step 1 ：The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Step 3 ：In this case, the given line has a slope of \(\frac{1}{5}\), so the slope of the line perpendicular to it is \(-5\).

Step 4 ：We can find the y-intercept \(b\) by substituting the coordinates of the given point and the slope into the equation \(y = mx + b\) and solving for \(b\).

Step 5 ：Substituting the values, we get \(b = -19\).

Step 6 ：Final Answer: The equation of the line that passes through the point \((-5,6)\) and is perpendicular to the line \(y=\frac{1}{5}x-5\) is \(\boxed{y=-5x-19}\).