Some possibilities since start of BCS

2019: LSU was preseason AP #6 so just outside of your list.
2013: Florida State was preseason AP #11.
2010: Auburn was preseason AP #22.
2006: Florida was preseason AP #7.
2003: USC (if you count it) was preseason AP #8.
2002: Ohio St was preseason AP #13.
2000: Oklahoma was preseason AP #19.
1998: Tennessee was preseason AP #10.

Despite all of the craziness of the 2007 season, LSU was the preseason #2.

To your point, it looks like we have to go back to before the internet era of recruiting really took off in the early 2000s to find where it was common for a team outside of the preseason top 5 won the title.

To okbar's point, the outliers since 2006 all had dominant quarterbacks (Newton, Winston, and Burrow).