The late hours DO bother you if you can’t get up in the morning. In future semesters you can try and schedule later classes. It’s hard for anything to wake you up when you haven’t had enough sleep - but one thing to try if it is dark when you have to get up is a light that gradually comes on which simulates sunrise and helps the brain transition to wakefulness. But again if your body is saying it needs more sleep it may not help.
Architecture can be competitive - you are sabotaging yourself when you stay up so late that missing classes is negatively affecting you classes and potentially your GPA. Working until 1 or 2 in the morning is one thing - 5 am is staying up all night and shouldn’t be needed regularly to finish work.