Beating Cincy might get BYU to 6. Maybe.
But you still have aTm (won't play in SEC championship game) and Florida ahead.
Making matters worse, 4 out of the top 5 teams are likely to play each other this year (Clemson-ND rematch in the ACC championship; Alabama-FL in the SEC championship). If/when those games happen, it's unlikely that any participant will get bumped out of the top 5 - they'll just trade spots like Clemson and ND did not too long ago.
There is no clear path forward for BYU, and playing Cincy wouldn't change that.