x^2 - 6x + 5 ≥ 0
Set this to 0
x^2 - 6x + 5 = 0 factor
(x - 5) ( x - 1) = 0 set each factor to 0 and solve and x = 5 and x =1
The solution to the original inequality will come from either of these two intervals (-inf,1] and [5, inf) or from the interval [1, 5]
Note that testing any point between x = 1 and x = 5 will make the inequality false
So.....the solution is x = (-inf, 1] U [5, inf )