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300 times.

In the ones place it occurs ten times per each 100 [5,15,25,...95] so 10x10 =100.

Then in the tens place it also occurs ten times each 100 [50,51,52,53...59]

We already counted 55 as one for the ones place and now we're counting 1 for the tens place.

In the hundreds place, from 500 to 599 there are 100 fives (we already counted the tens and ones places. So 100 + 100 + 100 = 300.

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