Determine the maximum or minimum value of the function:
$f(x)=-5 x^{2}+10 x-18$

Step 1 ：We are given the quadratic function \(f(x)=-5 x^{2}+10 x-18\).

Step 2 ：The maximum or minimum value of a quadratic function occurs at its vertex.

Step 3 ：The x-coordinate of the vertex of a quadratic function given in standard form is \(-b/2a\).

Step 4 ：In this case, \(a = -5\) and \(b = 10\), so the x-coordinate of the vertex is \(-10/(-2*-5) = -1\).

Step 5 ：We can substitute this value into the function to find the y-coordinate of the vertex, which will be the maximum or minimum value of the function.

Step 6 ：Substituting \(x = -1\) into the function, we get \(y = -5*(-1)^{2}+10*(-1)-18 = -13\).

Step 7 ：The y-coordinate of the vertex is -13.0, which is the maximum value of the function since the coefficient of \(x^2\) is negative, indicating that the parabola opens downwards.

Step 8 ：Final Answer: The maximum value of the function \(f(x)=-5 x^{2}+10 x-18\) is \(\boxed{-13}\).