If I don't set an alarm, I'll sleep up to 13 hours...is this normal?

It may possibly be normal for you. It may also be a sign of a sleep disorder or intolerance/illness.

However.

Considering that you usually get 5-6 hours of sleep during the week and you partied the night before, it is most likely sleep debit and/or exhaustion. If you are quite active during the week and on the weekends and don't have a regular sleeping patterns then your body is going to snatch sleep when it can and you will sleep for hours and hours until your body finishes getting you up and running again.

If you want to test it, try going a couple of weeks getting at least 7 hours of sleep a night, go to bed at the same time and wake up at the same time. If you can, ditch the alcohol, limit your tea/coffee after 2pm (it would be best not to have any) and avoid sugary, really high energy foods for dinner. Keep it simple but tasty.

If you are still crashing for 12 or 13 hours with a regular and healthy sleep pattern, then it would be a good idea to have a check-up.

Set Alarm For 6 Hours

During the week I only get 5 to 6 hours of sleep per night, but every Friday and Saturday I sleep for around 10 to 12 hours. I don't let it upset me, I just look at is as making up for all the sleeping in I can't do through the week. Nothing wrong with sleeping in late if you have nothing important to do that day.