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On an analog clock, there is one 5 that is always apparent.

On a digital clock, it depends whether or not seconds are displayed. If not, the hours position shows 5 twice per day, the tens of minutes position shows 5 once per hour or 24 times per day, and the minutes position shows 5 six times per hour, which is 144 times per day.

2 times/day + 24 times/day + 144 times/day = 170 times/day

If seconds are displayed, in addition to the 170 times/day you have in the tens of seconds position a 5 once per minute, which is 1440 (60 * 24) times per day, and in the seconds position you have a 5 six times per minute, which is 8640 (1440 * 6) times per day.

170 times/day + 1440 times/day + 8640 times/day = 10,250 times/day

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