Season 5 is my favorite season of Buffy, even more than 3. So many things about it are fantastic. Glory is my favorite big bad, the Key arc was extremely compelling, the plot twists were fun and kept my on edge and guessing about what would happen next, there were a lot of really strong episodes, some of the best in the entire series (The Body, the Gift, and a few others whose names I can't remember...Season 4 and 5 both had a disproportionate amount of the very best individual episodes IMO, many many good individual episodes).
Dawn? I adore Dawn. I'll admit she got to be a little annoying in Season 6, but in Season 5 I never once thought to myself that she was annoying while I watched it. I don't get why people say that, at least about S5 Dawn, I really don't. On top of that I really like her character and plot contribution and development from S5. I feel strongly about defending her, partly because so many people hate on her and I don't get where they are coming from.
And some of MT's performances in some S5 episodes are incredible. Like the episode Blood Ties where Dawn figures out she's the key and has the confrontation of sorts with Glory at the end. There are other episodes in S5 too that I thought to myself, "wow, this is an incredible performance, especially for someone so young." MT crushes it in quite a few episodes. Overall she was amazing.
Season 5 also has arguably the best acting performances from Sarah and Alyson too. Tara finally gets serious development and a greater role in the show, The Tara and Willow ship gets developed and the choice by the writers to do that really capitalized on the great and believable chemistry that existed between those two on screen, the writing in general is of such a consistently good quality in Season 5, Anya and Spike are both at their best in S5 too, I could go on and on about this season.
I like Glory (and the actress) a lot; I enjoyed the combination of her great godly power with her fatal character flaws. As a God in her proper and appropriate dimension, I imagine her character flaws would never have mattered or been a liability, and maybe she developed them over the many years of being an undisputed master. But I like how her personality traits translated into corporeal human form become fatal flaws, most of all because she doesn't know it, because she's never been in human form before and has always taken her invulnerability for granted, because she always could. It makes for a very interesting Big Bad if you ask me. I like many of Glory's soliloquys and boasting, partly because they are well written and partly because I really find fascinating the thought process of someone who is a type of God. It's not something you encounter every day! I really like all of Glory's interactions with Dawn throughout season 5, especially towards the end. I also like Ben insofar as the situation between Ben sharing a body with Glory effected Glory's psychology. And on and on.
The Knights of Byzantium were okay, I actually really kind of liked the idea but I didn't like as much the execution. I liked the added element of other good guys involved that were coming from a different position and were therefore bad guys in a way and at odds with the other good guys, the scoobies. I like the devout/pious and strict code-adhering and implied nobility of them. I wish the execution had been a little different though and that there had been more time to flesh out the details of them.
And I just realized I've been off topic the entire time and that I haven't even addressed the original topic.
My impression (at least on this forum) is that S3 is by a very wide margin the most popular choice for favorite season. After that, it might possibly be S2 by a slim margin over S5, or they might be tied. No one claims Season 1 as their favorite, a few people claim Season 4 as their favorite, a small but dedicated minority claim Season 6 as their favorite, and no one at all really claims Season 7 as their favorite. All this is just to say that Season 5 really isn't underrated, according to my observations, at least here on this forum. We could settle it once and for all with a poll to see who is second place. Maybe I'll do that myself.