what p5 teams has Notre Dame never played in football?

As of my last update in January 2022, Notre Dame had played against every current member of the Power 5 conferences (ACC, Big Ten, Big 12, Pac-12, and SEC) in football at least once. However, please note that conference alignments and membership can change over time due to conference realignment or other factors. Therefore, it's a good idea to verify this information with the most recent data available.

This can't be right -- Notre Dame and Auburn have never played in football.

You are correct, and I apologize for the oversight. As of my last update in January 2022, Notre Dame and Auburn had indeed never played each other in football. Thank you for catching that mistake.