Question

What is the solution set of {x | x < -3} ∩ {x | x > 5}?

Answer 1

& What is the solution set of {x | x < 2} {x | x ≥ 2}?

Answer 2

Drawing a number line makes this much easier to think about. x such that x < -3 means that x can be every number from \[-\infty\] up to -3. Because it is < -3 and not \[\le -3\] you know that -3 is NOT included. You can think about 5 similarly, but going in the positive direction.
Finally, remember that ∩ is the intersection. So take a look at your number line and identify which values are in both sets?