I thought the law was no alcohol after 5:00 am.
When I was there a few months ago, it was sort of followed. Bars would start "closing down" around 4:45 am but if you were already inside, especially on an upstairs or underground level, they would usually keep serving you until 6:00 am. The 24/7 pizzerias at Plaza Italia and next to the major train stations always sold alcohol no matter what hour, even with cops standing right outside in front.