The problem of the broken clock

Sorry, I'm in a philosophical mood today. Deal with it.

Suppose you have a clock that has never failed you during the many years that you've had it. You look at the clock, which reads 5:00 pm. As a result, you come to believe that it is indeed 5:00 pm. And you're right--it is 5:00 pm.

Now suppose that one hour passes. You look at the clock once more, which still reads 5:00 pm. Of course, it is now in fact 6:00 pm. It seems that your clock is broken.

According to Plato, knowledge is justified, true belief. On the one hand, one hour earlier you believed that it was 5:00 pm. You were justified in believing that it was 5:00 pm, for your hitherto reliable clock said so. And the time really was 5:00 pm. You had a justified, true belief that it was 5:00 pm. On the other hand, if the time had really been, say, 2:30 pm, you would have nevertheless believed it was 5:00 pm. And you would have been wrong.

So... did you know it was 5:00 pm? Or is Plato missing something?