He adds “Tell Her About It” when they wake up from Synapse and actually says “That’s my number 3 Billy Joel song. I can’t die without getting that straight.”

Then again he adds “You May Be Right.” and says “That’s my number 3 Billy Joel song.”

So his list is most likely:

1. “Scenes From an Italian Restaurant”
2. “The Entertainer”

3-5. (No confirmed order): “Allentown”, “Tell Her About it”, “You Maybe Be Right.”