A.T. Robertson Commentary 1 Corinthians 5:12

"For what have I to do with judging them that are without? Do not ye judge them that are within?" — 1 Corinthians 5:12 (ASV)

For what have I to do? (τ γαρ μοι; ). "For what is it to me (dative) to judge those without (τους εξο)?" They are outside the church and not within Paul's jurisdiction. God passes judgment on them.