(x – 5)2 - 5 < 20
(x – 5)2 - 5 - 20 < 0
(x – 5)2 - 52 < 0
(x - 5)(x + 5) < 0
The quantity on the left hand side is less than 0, so it is negative. It is possible only when either of (x - 5) and (x + 5) is negative (less than zero).
I Taking (x - 5) < 0
x < 0 + 5 or x < 5
II Taking (x + 5) < 0
x < 0 - 5 or x < -5
Both I and II show x < 0