A more natural English phrase would be "others exist."
And even better would just be "There are others."
I've never seen "There exist others", this might be translated as "There are others"
The correct answer to this question should definitely be "There are others." It would be rare indeed to hear a native English speaker say "There exist others."
Probably not everyday language, but very possibly you could see this in written form. I thought that "There are others" would be acceptable. Not surprised. I don't even expect to pass a lesson on the first try, any more.