In Argentina, the Buenos Aires province is divided in “partidos” and the other provinces are divided in “departments”. We have selected admin_level=5 for these divisions (admin_level=4 is used for provinces).
The problem is that I cannot see a complete partido in the screen. It appears that they can only be seen for zoom level 11 and greater, which is the same threshold than admin_level=6. For example, I cannot see the complete Salto Partido in http://www.openstreetmap.org/?lat=-34.218&lon=-60.265&zoom=11&layers=M and this is not the largest partido in the province. In other provinces, there are departments which are a lot bigger.
I think that the administrative borders that use admin_level=5 need to be drawn from zoom level 9 and greater.