I have recently started my new job and find that the 5:30pm finish is very inconvenient for me as it doesn't fit very well with the train schedule. It would mean me getting home much later than usual than if I finished at 5pm. This is not an issue for me now but when the sunset gets earlier, it may cause problems as my area isn't the safest to walk at night.
Would it be unreasonable to request flexible working hours so I could start at 8:30am to finish at 5pm (rather than the 9am-5:30pm), based on this scenario? Of course this would be done later, not right now as a new employee.
I wouldn't see that as unreasonable you're still working the same hours.
Depends on your employer, what your job is and whether someone would need to work 5-5:30 in your place. Most employers I've worked for have tried to accommodate people who rely on public transport though. Either way, you won't be able to change your shifts if you don't ask.