Assuming that once a number appears only once even if it remains for an hour - for example, the 5 in the hours place does not disappear and reappear at 5:00, 5:01, 5:02 and so on - it is 170 times over a 24-hour period.
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146
The number 5 will appear 146 times in 24 hours.
1:35
There are 93 such events.
On an analog clock with a 12-hour face: 44 times. On a digital clock: zero. (No needles.)