$x^{2}-6 x+5=0$

Step 1 ：We are given the quadratic equation \(x^{2}-6 x+5=0\).

Step 2 ：This is a quadratic equation in the form of \(ax^{2}+bx+c=0\).

Step 3 ：The solutions to a quadratic equation can be found using the quadratic formula: \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).

Step 4 ：In this case, \(a=1\), \(b=-6\), and \(c=5\).

Step 5 ：Substituting these values into the quadratic formula, we get \(x=\frac{-(-6)\pm\sqrt{(-6)^{2}-4*1*5}}{2*1}\).

Step 6 ：Solving this, we get \(x=\frac{6\pm\sqrt{16}}{2}\).

Step 7 ：This simplifies to \(x=\frac{6\pm4}{2}\).

Step 8 ：So, the solutions to the equation are \(x=1\) and \(x=5\).

Step 9 ：These are the values of \(x\) that satisfy the equation \(x^{2}-6 x+5=0\).

Step 10 ：Final Answer: The solutions to the equation are \(x=\boxed{1}\) and \(x=\boxed{5}\).