Final answer:
The solution set is all real numbers except -3 and 5.
Step-by-step explanation:
The solution set of the given inequality x ∈ (-∞,-3) ∩ (5,∞) is the set of all real numbers except -3 and 5. This means that any value of x that lies to the left of -3 and to the right of 5 on the number line will satisfy the inequality. However, the values -3 and 5 themselves are not included in the solution set. The solution set of an intersection of two sets A and B, denoted as A ∩ B, is the set of all elements that are both in A and in B. In this question, we are asked to find the solution set of x such that x is in the interval (-∞,-3) and also in the interval (5, ∞). Since these two intervals do not overlap, there is no element that is in both intervals at the same time. Therefore, the solution set is the empty set, which means that there are no real numbers x that satisfy the condition x ∈ (-∞,-3) ∩ (5, ∞).