Your insulation system is unlikely to perform well with 5°F "ice". So mostly that one gets shot first, with a much higher heat rate from ambient. Contents are colder... 'extra' cold does not buy you any better food protection.
Maximize insulation, minimize temperature difference.
I also had a crappy "cool bag" that I somehow thought was "water proof". The ice was melting, and the water was dripping out the bottom... so it could not conduct / convect heat to the walls of the "cool bag". One bag of ice lasted for almost a day, and food was cold the entire time. Don't get that with the typical styrofoam cooler.
David A. Smith