Albert Barnes on 1 Corinthians 5:12

For what have I to do, etc. I have no authority over them; and can exercise no jurisdiction over them. All my rules, therefore, must have reference only to those who are within the church.

To judge. To pass sentence upon; to condemn; or to punish. As a Christian apostle, I have no jurisdiction over them.

Them also that are without. Without the pale of the Christian church; heathens; men of the world; those who did not profess to be Christians.

Do not ye judge, etc. Is not your jurisdiction as Christians confined to those who are within the church, and professed members of it? Ought you not to exercise discipline there, and inflict punishment on its unworthy members? Do you not in fact thus exercise discipline, and separate from your society unworthy persons-- and ought it not to be done in this instance, and in reference to the offender in your church?

(b) "without" Mk 4:11