$5 x^{2}-125=0$

Step 1 ：Given the quadratic equation \(5x^{2} - 125 = 0\)

Step 2 ：This is a quadratic equation in the form of \(ax^{2} + bx + c = 0\). The general solution to a quadratic equation is given by the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

Step 3 ：In this case, \(a = 5\), \(b = 0\), and \(c = -125\). We can substitute these values into the quadratic formula to find the solutions for \(x\)

Step 4 ：Calculate the discriminant \(D = b^{2} - 4ac = 2500\)

Step 5 ：Substitute \(a\), \(b\), and \(D\) into the quadratic formula to get \(x1 = 5.0\) and \(x2 = -5.0\)

Step 6 ：The solutions to the equation are \(x = 5\) and \(x = -5\). These are the values of \(x\) that satisfy the equation \(5x^{2} - 125 = 0\)

Step 7 ：Final Answer: The solutions to the equation are \(x = \boxed{5}\) and \(x = \boxed{-5}\)