May I ask professors to reschedule two back to back night classes from 4:30PM to 9:00PM? As a graduate school student, I have two professors teaching two separate classes that go from 4:30PM to 5:50pm and 6:00pm to 9:00PM. This happens every one day of the week.
I'm not sure whether I can handle concentrating for 5 hours and I have the option to not take a class but it would delay graduating by a semester.
Do I negotiate with the professor to reschedule or do they have the power to deny it?
Academic timetabling is a notoriously difficult problem. Professors have several classes to teach, students have several classes to attend. There are restrictions related to classroom sizes, specific equipment (e.g. computer labs). Some professors may have individual restrictions, e.g. can only teach on specific days or hours due to other commitments.
Normally, Professors do not decide their own timetables, but submit their preferences to the Timetabling Office, which then generates a timetable for everyone. Students can also try to submit their requests, but usually as a groups (cohorts), not individually. If you are not happy with your timetable, it is definitely worth trying to change it, but bear in mind that it may not be easy.
However, if you class is scheduled up until 9pm, which is significantly beyond the core hours, you actually have a much better chance of having this class rescheduled, particularly if any of other students attending the same late class have caring responsibilities. Your Student Rep / Student Union Rep / Athena Swan Rep (in the UK) might be able to help you with the process.