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5 appears 170 times on the 24-hour clock, and the same number on the 12-hour clock
There are six times that theĀ 5 is in the units of the minutes (eg 01:25) each hour, so 5x24 timesĀ over 24 hours (144).
The 5 appears in the tens of minutes (eg 12:50) 24 times in 24 hours.
The 5 appears in the hours section (eg 05:00) twice.
In total, that is 144+24+2 = 170 times
The answer is the same for the 12 hour clock, because there's just two 5 o'clocks instead of 05:00 and 15:00.