Explanation:

The correct answer is option 5 i.e. BACDE.
Explanation
We can look into the sentence the following way:
"We know that the finest (A)__
that air pollution has been (B).
stress hormone (D)__
from dirty air can reach the brain via both the bloodstream and the nose, and damage to nerve cells and to changes in
_in increased [brain] (C)__
which have been (E)____________ to poor mental health," Braithwaite said.
Inflammation is a localized physical condition in which part of the body becomes reddened, swollen, hot, and often painful, especially as a reaction to injury or infection.
It is clear that (C) and (D) has grammatically and meaningfully correct words. Also (E) justifies its bold word. There is an adjective before A and this means that a noun should follow that.
Particulates mean matter in the form of minute separate particles.
Implicated means bore some of the responsibility for (an action or process)./ show (someone) to be involved in a crime.
Hence A and B should be interchanged.
Correct sentence: We know that the finest (A)particulates from dirty air can reach the brain via both the bloodstream and the nose and that air pollution has been (B)implicated in increased [brain] (C)inflammation, damage to nerve cells and to changes in stress hormone (D)production, which have been (E)linked to poor mental health," Braithwaite said.