When the question stem is of the form,
"the author mentions ____ in order to"
"the author's reference to ____ serves to"
"the author does ___ primarily to"
the test is asking "how does this specific detail relate to the broader point/purpose of the surrounding sentences?"
I think of these as "bookend" questions, because the correct answer is almost always a paraphrase of the sentence that came before or after the specific lines/detail we're asked about.
What are the bookend ideas here?
The previous idea was stating that increased use of fossil fuels will have a negative impact on health. Lines 5-9 give an example to support that claim.
The following idea brings up renewable energy as a potential solution to this problem. So we might say that lines 5-9 give us an example of a specific problem that renewable energies might avoid.
However, when they ask this type of question about a sentence that says "for example", the correct answer is almost guaranteed to paraphrase the previous sentence. Writers use "for example" to support their previous point.
A) previous claim was not about climbing energy rate but about how climbing fossil fuel usage affects public health.
B) lines 5-9 don't undermine, they support the previous sentence.
C) previous sentence was not about a timeframe or about renewable energy.
D) yup, this sounds like a paraphrase of the previous sentence. "Fossil fuels may damage human and environmental health" is a decent match for "fossil fuels are a problematic source of energy". And "offer evidence" / "substantiate a claim" / "lend credence to" are the types of phrases we want to hear about a 'for example' sentence.
E) lines 5-9 have nothing to do with "localized involvement", and this answer choice does nothing to reinforce the sentence prior to lines 5-9.
(D) is our answer.