Time Conflict Algorithm in PHP/Laravel?

I am currently creating an online registration web app that will allow students to register for classes online. The problem that I am now encountering is creating the time conflict algorithm.

As registration goes, every student should be able to register for at least 5 courses, but these courses cannot be all at the same time. So each time a student registers for a class at say 12:00pm - 1:00pm, the next class shouldn't be at the same time, it should be before or after this currently registered class. I have no idea on how to successfully implement the algorithm to get this done. Thank you very much in advance.