Just to piggy-back on JP's math (and make a couple of corrections):
There are actually 39 bowls this year, since the Poinsettia Bowl shut down. So only 78 teams will go bowling.
Only 8 spots remain open.
There are 4 games between 5-win teams this weekend (UCLA vs Cal, Colorado vs Utah, Indiana vs Purdue, Old Dominion vs MTSU). The winner of each of these games will become bowl-eligible.
So, in reality, only 4 spots remain open.
Of the teams sitting currently sitting at 5 wins, the following are ranked above Tennessee in APR:
Duke, Minnesota, Georgia Tech, MTSU*, Utah*, Indiana*, Cal*, Buffalo.
MTSU, Utah, Indiana, and Cal are on both lists. So, even if we assume that everything works out in UT's favor, and the teams that are behind UT in APR (UCLA, Colorado, Purdue, and ODU) all lose, it won't matter, because Duke, Minnesota, GT, and Buffalo would be guaranteed to get the 4 remaining bowl invites before UT.
Yup.