Jamieson, Fausset and Brown on 2 Corinthians 13:5

5. Examine--Greek, "Try (make trial of) yourselves."

prove your own selves--This should be your first aim, rather than "seeking a proof of Christ speaking in me" (2Co 13:3).

your own selves--I need not speak much in proof of Christ being in me, your minister (2Co 13:3), for if ye try your own selves ye will see that Christ is also in you [Chrysostom], (Ro 8:10). Finding Christ dwelling in yourselves by faith, ye may well believe that He speaks in me, by whose ministry ye have received this faith [Estius]. To doubt it would be the sin of Israel, who, after so many miracles and experimental proofs of God's presence, still cried (Ex 17:7), "Is the Lord among us or not?" (Compare Mr 8:11).

except ye be reprobates--The Greek softens the expression, "somewhat reprobates," that is, not abiding the "proof" (alluding to the same word in the context); failing when tested. Image from metals (Jr 6:30; Da 5:27; Ro 1:28).