is there a way to look up your previous opponent?...say 4-5 games back, to play against again?
Only if you win, then you will see on your profile page who you beat. If you lose, I don't think it will show up anywhere.
If you are a mobile player on the app , playing head to head , in the coin rooms , you can never see who you had previously played
One way would be to invite him as a friend during the game or shortly after,
or take the old-fashioned route of paper and pen ;)