After taking note of Joe's 4 consecutive race podium streak listed above, I hired the stats department to do some digging. As it turns out, this is the first time ever in 36 Sprint Cup series races that any driver has finished four consecutive races with a podium finish. Three consecutive races with a podium finish has happened 5 times before:
Droptop2001gt - S1, Races 1-3
ACDCROCKS123 - S1, Race 15 - S2, Race 2
Homeslice47 - S2, Races 9-11 (the only All-Chase streak)
ACDCROCKS123 - S2, Race 12 - S3, Race 2
Droptop2001gt - S3, Races 7-9 (current streak)
If you loosen the requirement from consecutively scheduled races to just consecutive starts, ACDC runs away with the all-time record. ACDC scored a podium finish in 9 consecutive starts, a feat that is almost certainly never going to be matched. That streak started in the final race of season 1, extended through all six of his starts in season 2, and ended with the second race of this season. His results during the streak were as follows: 1, 2, 2, 1, 2, 3, 2, 1, 2. You should notice that there is only one third place finish in the entire group, which makes it even more amazing.
Joe's current streak of 5 consecutive finishes with a top 5 is impressive, but far from the record. Homeslice47 went eleven consecutive races with a top-5 finish, stretching from races 2 through 12 of season number 2. The season-opening Daytona 500 was the only race in the entire 12-race season in which Homeslice failed to record a Top-5.
Other notable consecutive Top-5 streaks:
Droptop2001gt - 9 races: S1, races 1-9
Droptop2001gt - 7 races: S1, race 11 - S2, race 2 (these two streaks had only a sixth place finish at Indy between them, a combined 17 consecutive top-6 finishes)
JoeOfTheFire - 6 races: S2, races 7-12 (8-12 were all Chase Races for S2)
RFLX - 5 races: S1, races 11-15 (All Chase races for S1)
If you loosen the requirement here to just consecutive starts with a top 5 finish, these results get added:
RFLX - 13 starts: S1, race 1 - S2, race 4
ACDC - 10 starts: S1, race 15 - S3, race 4 (current streak)
Joe - 6 starts: S1, races 4-11
Homeslice - 6 starts: S1, races 7-15