The reason for him saying "five predecessors" instead of six is that, as stated in the first movie, the first matrix was designed as a paradise - that no one would accept, and everyone started trying to wake up from. It didn't last long enough for The One to arise, but instead was a disaster and came unravelled, so it was re-designed to mimic the "real world" of an era past.

I wonder which other eras the other matrixes (matresies?) were patterned after, as opposed to the late 20th century, as Neo's one was. Apparently one was a circa 18th century Transylvania, since there were using vampires and werewolves as agent programs to police the place (as seen in Reloaded - the Merovingian's rogue programs were described as left over from an earlier version of the Marix). Perhaps Van Helsing was originally entitled "The Matrix: Beta Test"?