Here's what I'm thinking.
1. Zootopia
2. Kubo and the Two Strings
These two are guarantees. They've got the bulk of the critics awards, generally fantastic reviews, and both are exemplary in their respective mediums (computer and stop motion, respectively.) There's no way they miss.
3. Moana OR Finding Dory
This is a bit more tricky. I think it's likely that Moana gets the nomination rather than Dory, the circumstances of Zootopia already being there, so it's not like WDAS will get shut out if Moana misses, mean that we probably can't count Pixar getting a nomination. It's not as if Dory isn't an undeserving film in its own right. Critically, the films are close (95/7.9 for Moana and 95/7.6 for Dory), so it could be a tossup.
However, I think back to 2014, and the upset when Lego didn't get a nomination, despite critical raves. I've argued that it makes sense from a budgetary standpoint, but I also wonder if there might have been a case of tactical voting. Where animation branch members might have felt it would have been a deserving nominee, but also realized it was guaranteed to win if it did get a nom, when they saw other films (any of the other films, perhaps) as more deserving winners.
There's no way to prove this, of course, but it's possible that Dory beats Zootopia as the winner if it gets a nomination, and I doubt anyone in the animation branch feels Dory is a more deserving winner. Moana isn't likely to pull an upset in the same way.
(In contrast to '14, if Dory misses a nom, nobody will cry foul.)
4 & 5.
Two spots left, and they'll be filled by indies. We've had a swath of them this year, so there's no lack of hopefuls. I'd rank their chances thusly:
a. My Life as a Zucchini
b. The Red Turtle
c. Your Name
d. April and the Extraordinary World
e. The Little Prince
f. Miss Hokusai
g. Phantom Boy
h. whichever misses between Dory and Moana
I almost put Zucchini as slot 4 and left the others for the fifth, but there are so many possibilities here, I won't really be surprised if any miss it.
Still, Zucchini is stop motion, which gives it a pretty massive medium bump.
The Red Turtle is partially Ghibli, so that may come into play.
Your Name does have some pretty great critical response, though again, as with Lego, that's no guarantee. A lot might come down to how well regarded the character animation is. Shinkai does some phenomenal stuff with backgrounds and such, but his character work isn't jaw-dropping in comparison. Outside of Ghibli, anime in general doesn't seem to be well regarded.
April feels like it's a bit outside the top three. It's got some great animation and character work, though, plus some delightfully off-kilter worldbuilding that brings to mind Miyazaki blended with European influences.
The Little Prince, I don't know. The story itself has some great stop motion work, which is in its favor. But it's got the less well regarded framing story, which might ding it as lower budget computer animation. Plus there's those distribution woes. Had it gotten a wide-ish release, I'd put its chances as much more likely.
Miss Hokusai has the problem of running in the same year as Your Name, so it's got a much higher profile and probably better regarded anime film competing with it. Still, it's probably not completely dead.
Phantom Boy is from the same studio and directors as A Cat in Paris, which got a fairly surprising nomination in 2011. It's got about the same blend of off-kilter charm and suspenseful adventure, but it also is in a much more competitive year.
And we're back to Dory and Moana again. I put this here mostly because it's possible that both of them do get a slot, but I consider such a thing slim.
Part of the reason I don't want to count any of these out is what I'd call the Boy and the World effect. It doesn't matter how low profile something is. The animation branch can still give it a push if they like it enough.