~4-5 stories is totally sufficient to be "dense" compared to most of the US. Cities in the US sprawl absurdly flat. Consider that Paris is one of the densest cities in the world, and famously has almost no tall buildings.
If Paris is a model for the world, I don't want this world.
Numbers from https://versus.com/en/berlin-vs-london-vs-new-york-vs-paris/....
Edit: And a considerable amount of land given over to parks, museums, churches, and other non-residential spaces.
So yeah, Paris is dense, but if you compare block by block the differences are smaller.
[1] https://de.wikipedia.org/wiki/Verwaltungsgliederung_Berlins