y=sqrt(x^2-6x+5)
What is under the square root sign is >=0
Therefore,
x^2-6x+5>=0
We factorise the inequality
(x-1)(x-5)>=0
Let f(x)=(x-1)(x-5)
We build a sign chart
color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaaaa)1color(white)(aaaaaaaaa)5color(white)(aaaaaaa)+oo
color(white)(aaaa)x-1color(white)(aaaa)-color(white)(aaaa)0color(white)(aaa)+color(white)(aaa)0color(white)(aaaa)+
color(white)(aaaa)x-5color(white)(aaaa)-color(white)(aaaa)0color(white)(aaa)-color(white)(aaa)0color(white)(aaaa)+
color(white)(aaaa)f(x)color(white)(aaaaa)+color(white)(aaaa)0color(white)(aaa)-color(white)(aaa)0color(white)(aaaa)+
Therefore,
f(x)>=0, when x in (-oo,1] uu [5,+oo)
graph{sqrt(x^2-6x+5) [-10, 10, -5, 5]}