Definition of Done
Let say a user story has 10 definitions of done and from 10 definitions of done, the development team just finished 5 of 10, does it count as done or not?
The Definition of Done is not something that is associated with a particular user story, or any other type of Product Backlog Item. A team maintains a Definition of Done that describes what must be complete for a Product Increment to be considered Done. Some items may apply to individual Product Backlog Items while others may apply to the integrated Product Increment.
What you describe sounds like acceptance criteria. I've often seen individual work items have 1 or more acceptance criteria that are unique to that particular work item. While the Definition of Done applies to the team's work, these acceptance criteria provide additional details and guidance as to how to determine that the work item is done. Work is only done when all criteria for completion, whether from acceptance criteria, the team's Definition of Done, or another source, are met.
Let say a user story has 10 definitions of done and from 10 definitions of done, the development team just finished 5 of 10, does it count as done or not?
Would it be immediately releasable without need of further work, and of sufficient quality?