-x^2 + 4x - 5 ≤ -2 add 2 to both sides
-x^2 + 4x -3 ≤ 0 multiply through by - 1 and reverse the inequality sign
x^2 - 4x + 3 ≥ 0 factor
(x - 3) ( x - 1) ≥ 0
Note that when 1 x < 3 ......the inequality will be false
So the solution is (-inf, 1}] U [3, inf )