Alex
I don't know how you are adding your students to the Moodle site. If you are using a text file you can add extra columns to enroll in the course. See documentation here. You could also use this to enroll them in the cohort if you wish to do that.
The nice thing about cohorts is that you can easily add another course you want them all in if you need to without having to go through the process again. I have never had to put 5000 students in one cohort. Haven't heard of any problems with it. Perhaps someone else knows something I do not.