Reading the question: We have a long prompt and a short stem, so we check the stem. It says "resolve a discrepancy." That's the same as "explain." As discussed in Osprey Prey and Caller Complaints, since we are explaining, we should identify the two parts of the so-called "discrepancy." The correct answer will need to address both parts, without contradicting any of the facts given.
Creating a filter: "Perplexingly" is an important word, because it allows us to parse the prompt into two parts. The second, shorter part is that sharks must be protected from overfishing. Why is that perplexing? Because of whatever the main point of the first part is: sharks live longer than expected. We'll look for something that connects logically to both parts: 1) sharks live longer than expected, and 2) they must be protected.
Applying the filter: (A) doesn't connect to the sharks' age. Choice (B) just restates part of the prompt. Choice (C) just restates the other part of the prompt. Choice (D) doesn't connect to either portion of the discrepancy. Choice (E) touches on both parts: it says that if sharks are older than we thought, there are fewer of them than we thought. That's a good reason to protect them from overfishing.
Logical proof: A logical proof is not always possible on "explain" questions, but we can use the negation test to confirm (E), in this case. Suppose that sharks reproduced more quickly than had previously been assumed: that would lessen the need to protect sharks. Since the negation would add to the mystery and contradict the opinion of "some parties," we have confirmation the non-negated (E) would, indeed, resolve the mystery. The correct answer is (E).
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