Intuitively I felt like we’d want to find pairs of 5s and 2s to make 10s. Why is it the case that we are only looking at 5s?

You can look at pairs of two. However, you’ll quickly find that there are a lot more twos than fives. The problem here is that to get pairs of 10, you need pairs of **both** 5 and 2 - and hence the number of trailing zeros would be restricted by the number of 5s.

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understood, thank you!