Answer
$\text{$x-$intercepts: } \{
1, 5 \}
$
Work Step by Step
Setting $y=0$ and solving for $x$ using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), then the $x-$intercept/s of the given equation, $
y=x^2-6x+5
,$ is/are
\begin{array}{l}\require{cancel}
x^2-6x+5=0
\\\\
x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(1)(5)}}{2(1)}
\\\\
x=\dfrac{6\pm\sqrt{36-20}}{2}
\\\\
x=\dfrac{6\pm\sqrt{16}}{2}
\\\\
x=\dfrac{6\pm\sqrt{(4)^2}}{2}
\\\\
x=\dfrac{6\pm4}{2}
.\end{array}
Hence, the $x-$intercepts are
\begin{array}{l}\require{cancel}
\text{$x-$intercepts: } \{
1, 5 \}
.\end{array}