The solution set is [tex]x<1[/tex] or [tex]x>5[/tex]. Refer to attached file for the graph
Factoring the quadratic expression, we find that
[tex]x^2-6x+5=(x-1)(x-5)[/tex]
So, the quadratic inequality can be expressed as
[tex](x-1)(x-5)>0[/tex]
We have two possible cases: both of them is greater than zero or both of them is less than zero. That is,
[tex]\begin{cases} x-1>0 \\ x-5>0\end{cases}or \begin{cases} x-1<0 \\ x-5<0 \end{cases}[/tex]
Solving each, we get
[tex]\begin{cases} x>1 \\ x>5 \end{cases}or \begin{cases}x<1\\x<5 \end{cases}[/tex]
In the first case, we get the solution [tex]x>5[/tex], and in the second case, we get the solution as [tex]x<1[/tex].
