Five floors is the maximum allowed for wood buildings by code in most jurisdictions in the United States.
Los Angeles recently started allowing seven floors. Here's the result:
http://cdn.abclocal.go.com/
Those flames are several hundred feet tall.
It was a long horizontal building, 7 stories of wood, like a skyscraper on it's side, and the fire spread horizontally. Imagine if it were as tall as it was wide, the flames would have been over a thousand feet tall.
Built with all the modern fireproofing materials and requirements.
This building wasn't fully built, but was up to the full height, so luckily not open yet and no occupants were killed.
They can add as much fire prevention as they want to wood, and it might actually prevent some small fires from turning into big fires, but once the fire starts and takes hold of a tall wood structure, all bets are off. Your fireproofing better be solid rock.
http://cdn.abclocal.go.com/
Also, most of the tall wood buildings in Los Angeles are extremely ugly. Developers who skimp on materials usually don't hire quality architects.
If downtown LA gets hit with a 6 magnitude earthquake, you can expect to see several of these burning at the same time, probably with people in them, and no water to fight it because the water mains will most likely break in the quake. 110 buildings burned down in the Northridge quake fire.