What five passages from The Lost City of Z have significant meaning and hold great importance to the overall plot?

You have been given and interesting assignment about this particular book.  Yes, The Lost City of Z: A Tale of Deadly Obsession in the Amazon, written by David Grann, is a story about true "deadly obsession" that traces Percy Fawcett's exploration of the rainforest along the Amazon river.  There are quite a few quotes that further the plot.  Let us talk about a few:

Years later, another member [of the Royal Geographical Society] conceded, "Explorers are not, perhaps, the most promising people with whom to build a society. Indeed, some might say that explorers become explorers precisely because they have a streak of unsociability and a need to remove themselves at regular intervals as far as possible from their fellow men.

In looking for the "lost city of Z," many men (not just Fawcett) are lost in the Amazon.  This quotation talks a little bit about why (and about the social errors of these men).  Needing to remove himself from society, then, is an interesting reason why Fawcett would apply himself to this quest.

You know, I had a lot of romantic notions about the jungle and this kind of finished that.

This is another quotation that shows the original exploration of the Amazon by Fawcett was an obsession based on a romantic type dream.  The reality of the Amazon was quite different, as the book shows in graphic detail due to the loss of (not only Fawcett) but also many other explorers.  How did these explorers die?  The book delves into that idea as well:

They marched like madmen from place to place, until overcome by exhaustion and lack of strength they could no longer move from one side to the other, and they remained there, wherever this sad siren voice had summoned them, self-important, and dead.

The obsession of this exploration of the Amazon adds to the "siren voice" here.  If you grasp the allusion to the sirens, then you know that sirens are the females who would sing sailors to their deaths on the rocks within the tales of Odysseus.  These explorers were tempted too, by their own obsession.  They all seemed to end up "self-important, and dead" after they blindly marched along their quest.