Depends on your mower and deck size, too...
Generally speaking the larger the deck the higher you should cut but some mowers allow higher settings than others.
My mowers are set to the highest each will go, not all mowers can go as high.
I cut at 4" with my 21" Honda and 48" Toros, and 5.75" with the 60" Ztr's.
You will usually have to get into some pretty wide decks before getting much past that 4" setting, although there may be a few smaller decks that allow it.
I'm in zone 8 where it's mostly fescue, some zoysia and some bermuda.
Oh and we have crap grass as well, plenty of it too.