Right away, we should notice that A and B both start with "due to", while C, D, and E all start with "because of". An important rule to have memorized is that "due to" can only modify a noun, while "because of" can only modify a verb.

We want to say that the moisture exhaled by tourists had the effect that the chambers "were closed"-a verb. This means that we want to use "because of". (In fact, if we use "due to", the sentence reads that the moisture exhaled by tourists had the effect of "cleaning and repair" ... which doesn't make a lot of sense.) So we can eliminate A and B.

Scanning C, D, and E, we see that E is the shortest answer, so we should already be leaning toward that one. Looking back at our original sentence, we see that the last portion of the sentence is not underlined and that it starts with a conjunction. Whenever we see that we have a series (a list of two or more items connected by a conjunction) where part of the series is underlined and part is NOT, we should immediately start looking for parallelism issues. The last item in the series ("fungus was growing on the walls") is not underlined, so we want the underlined item to match it-so "noun past continuous verb". Looking at our options, we see that only E has the correct structure ("salt from the stone was crystallizing") and must be correct.