I'm not sure if the fifth dungeon will actually be a divine beast... there is a mention of there being some sort of ancient facility beneath Hyrule Castle, so I think it'll be that.
If there was a fifth divine beast, then I think it would have been mentioned at some point, but it's possible they had begun work on one, and left it unfinished, in which case it might have been left it in the facility beneath the castle, so we might still see it, even if it's not operational.
It is a safe bet that a fifth divine beast would have been built specifically for one of the races, which leaves us with the Sheikah, Hylians, and Kokiri/Korok (we don't know when they changed form in this timeline).
I doubt the Sheikah would have made themselves one until they made one for each of the other races, so that basically rules them out.
The Hylians I would have thought would be the first to get a divine beast, if they got one at all, so I think they're less likely... but I'd say it would probably have been a lion, as a nod to the King of Red Lions.
The Kokiri/Korok I think would be most likely (we even have a Korok with a unique ability (potential champion) already... Hetsu)... and if I was to pick an animal for it to be based on, I'd probably say it would be some sort of monkey, as a nod to the monkeys in TP.