Let \[ f(x)=-5 x^{2}+5 \] Find the equation of the tangent line to $f(x)$ at $x=-7$. \[ y= \]

Step 1 ：Given the function \(f(x) = -5x^2 + 5\)

Step 2 ：Find the derivative of the function, \(f'(x) = -10x\)

Step 3 ：Substitute \(x = -7\) into the derivative to find the slope of the tangent line, \(m = 70\)

Step 4 ：Substitute \(x = -7\) into the original function to find the y-coordinate of the point of tangency, \(y = -240\)

Step 5 ：Use the point-slope form of a line to find the equation of the tangent line, \(y - (-240) = 70(x - (-7))\)

Step 6 ：Simplify to find the equation of the tangent line, \(y = 70x + 250\)

Step 7 ：\(\boxed{y = 70x + 250}\) is the equation of the tangent line to \(f(x)\) at \(x=-7\)