5 floors was pretty standard across Europe, from Paris to Kyiv, in the age before elevators, as it was about the maximum height most folks were willing to walk up the stairs. Though, in Paris a lot of the 6th floors (where lots of the typically small studio apartments are found) were originally constructed as the maids' quarters.

In Seattle we hav a lot of 4+1s: a concrete 1st floor and wooden 4 floors above that (some kind of code thing). The first floor is usually retail, however.