How to persuade the class teacher to agree to take five days off to attend a job fair for college students in other places, and how to make the conversation harmonious?

Then you should be patient and tell him clearly that you will go without affecting your study. And try to make him feel that if you are not allowed to go, he will affect your employment opportunities. That depends on your personal way of speaking. My classmates have also encountered this situation, say more good things. Success belongs to persistent people. But it would be much easier if these five days included weekends.