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At 11:55, provided everyone heard what was said, they would all know that at least one hat is red and they would all see four red hats and not know what there’s was. If someone saw all blue hats, they would know their hat is red and leave the room at 12:00. But at 12:00, no one leaves the room. That means they know they all saw at least one red hat. But if we look at two people we see that red=4 for both of them, but neither leaves the room. Which means that I know if no one left the room that that person saw a red hat on mine as well and I can leave the room at 13:00. Of course, everyone else should be able to follow that logic and everyone would leave the room at 13:00.
This is of course all subject to the five persons in the room having any brain. It is probably just a likely to have a room of five dolts that couldn't figure this out and they would all stave to death in the room, or that the world is eaten by a giant space goat prior to them figuring it out.
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