Assuming you meant
f(x) = x^2 - 6x +5
this is a parabola shifted to intercept the y-axis at +5.
The roots are
x^2 - 6x + 5 = f(x)=0
(x-1)(x-5) = 0 This is because we want to know what is going on when the y value for the equation is 0 (f(x) set to be 0)
-----> x = 1, 5 when y (f(x)) = 0
If you imagine this graph, it is a parabola with a y-intercept of 5 and x intercepts of 1 and 5.
the peak (minimum in this case) of the parabola is
2x - 6 = dy/dx = 0
x = 3 ------> 3^2 - 6(3) +5 = -4
minimum at (3,-4)
