And then not again until the 54th #AcademyAwards, for the films of 1981:
Reds - Warren Beatty
Atlantic City - Louis Malle
Chariots of Fire - Hugh Hudson
On Golden Pond - Mark Rydell
Raiders of the Lost Ark - Steven Spielberg

Next was the 78th #AcademyAwards, for the films of 2005:
Brokeback Mountain - Ang Lee
Capote - Bennett Miller
Crash - Paul Haggis
Good Night, and Good Luck - George Clooney
Munich - Steven Spielberg

Just those four times that the 5 Best Director nominations match the 5 Best Picture nominations. Unless some day they go back to only 5 BP nominations again.
I feel bad that I missed out the Peyton Place Director up at the very top of this thread. This is for you, Mark Robson!