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You're correct. It's 3, not 5.

Was it on the bottom half of the front page? If so, it might fall under the moderator-curated group that the author mentions. Or, if it was lower, it might have been there earlier.

This story is currently at position 5 with only 3 points:

https://news.ycombinator.com/item?id=29024572

From my experience, its the speed that a post gets points/comments that matters. If you get three quick enough you should get on the front page.