At what point(s) does the graph of the function shown below have a horizontal tangent?
\[
x^{2}+y^{2}=-10 x
\]
There is a horizontal tangent at the point(s)
(Type an ordered pair. Use a comma to separate answers as needed.)

Step 1 ：Given the equation \(x^{2}+y^{2}=-10 x\), we can rewrite it as \((x+5)^{2}+y^{2}=25\). This is the equation of a circle with center at (-5,0) and radius 5.

Step 2 ：A horizontal tangent to a circle occurs at the top and bottom of the circle. Therefore, the points where the graph has a horizontal tangent are when y = 5 and y = -5.

Step 3 ：Substitute y = 5 and y = -5 into the equation of the circle to find the corresponding x values. The solutions for x when y = 5 and y = -5 are both -5.

Step 4 ：Therefore, the points where the graph has a horizontal tangent are (-5, 5) and (-5, -5).

Step 5 ：Final Answer: The points where the graph has a horizontal tangent are \(\boxed{(-5, 5)}\) and \(\boxed{(-5, -5)}\).