Speaking about breaks between classes in American English you could say that it´s the "recess" but I think they can talk about break between classes (break between lessons in Br. English - I have learned).
It may vary, of course. If the student doesn´t change from a classroom to the other (they are in the same classroom with the same teacher) it can be called recess, but break between classes/lessons rings less formal to me.
There are some differences from school to school, and when there are changes from classroom to classroom, students may say that it´s the "passing time".
Anyway, other more advanced-level members of the Forum may improve this answer, confirm, or add more insights.
Informally, I would say that "...break between classes" or "...the next break between classes" would do.