There's a course near where I live, Saddleback Ridge, that has back to back par 5s, in fact 3 of four consecutive holes are par 5.
12 - par 3, 200
13 - par 5, 560
14 - par 3, 180
15 - par 5, 540
16 - par 5, 550
17 - par 3, 200
Number 15 & 16 run in opposite directions, the 15th teeing off from a ridge to the valley about 80-90 feet below, 16 climbing back up the ridge the last 150 yards or so.
Only course I've ever seen with 6 holes in a row that aren't par 4 . It is one of those 6/6/6 courses.