This question CANNOT be an official GMAT question - the statements contradict each other! Beware of studying from GMAT sources that do not conform to GMAT rules!
But before we get to that, let's analyze how we
would approach a legal absolute value / inequality question...
When looking at absolute values with inequalities, I find it most helpful to think in terms of a number line. Where will (x - 5) have a distance from 0 of more than 4?
Our real question:
is x > 9 or x < -1 ?
(1) x^2 > 4
Be careful with squares and inequalities! We need to think about the positive and negative case, and thus flipping the signs. Think about this on a number line:
As we can see, there are values that will give us a "yes" answer to our question (e.g. 10), and values that give us a "no" answer (e.g. 5). Insufficient.
(2) x^2 < 1
Again, let's see this on a number line:
As we can see, this entire range satisfies x < 1, so it's Sufficient.
HOWEVER!!!... on a real GMAT question, the statements can't possibly contradict each other, because they have to both be TRUE. It's not possible for x^2 to be both greater than 4
and less than 1. These statements contradict each other, therefore this is an impossible question.
