1. May/Should I ask a question?
The correct modal verb is May.
2. You should/need stay at home if you're ill.
The correct modal verb is should.
3. You don't have to/mustn't be rude to your teachers.
The correct modal verb is mustn't.
4. Parents can't/don't have to park their cars in front of the school gates.
The correct modal verb is can't.
5. You may/have to ask for permission to leave the classroom.
The correct modal verb is have to.
Ответ: May, should, mustn't, can't, have to