The deaths of Thorin, Fíli, and Kíli, and particularly the Final Speech of the first:
"There is more in you of good than you know, child of the kindly West. Some courage, and some wisdom, blended in measure. If more of us valued food and cheer and song above hoarded gold, it would be a merrier world. But sad or merry, I must leave it now. Farewell."
Fíli and Kíli dying is understated in itself, but throughout the book the narration makes it clear that they're the youngest of the group, which, when you know about how Tolkien fought in World War I, makes the terrible waste of young men's lives all the more poignant.
The animated movie
Although it's pretty short and limited (may or may not because of Limited Animation), Thorin's death scene is played as sad as possible, with Thorin apologizes and makes peace with Bilbo for calling him a coward before. Also, the Death by Adaptation for some other dwarves.
Bilbo: How many of our original company are left? Gandalf: Only seven. Bilbo: What about Thorin? Gandalf:Soon it will be six.
In fact, Peter Jackson decided that if Saruman couldn't come to Middle-Earth, Middle-Earth would come to him. Lee's work was shot on a sound stage and merged into the relevant scenes, so that he never had to leave the UK.
The music video for The Battle of the Five Armies' official song, "The Last Goodbye" sung by Billy Boyd, has scenes from both The Hobbit trilogy and The Lord of the Rings trilogy. It also includes behind the scenes footage showing Peter Jackson hugging the cast members from both trilogies after filming had wrapped. The song's content and video really hammers in the fact that The Battle of the Five Armies is truly the last Middle Earth film.
The Appendices of The Battle Of The Five Armies has a bonus video that pays tribute to cinematographer Andrew Lesnie, who died of a heart attack in April 2015. Philipa Boyens mentions that the first people who sent their condolences were the cast who'd worked with him over the years, saying that it shows how much of a family they were. The other person interviewed in the video was Christopher Lee, who said that he considered Andrew to be the greatest cinematographer he'd ever worked with (and considering how many films he'd been in, that's saying a lot). The tear jerker factor is raised even higher when you remember that this was only two months before Christopher himself sadly passed away, as well.