What does 2 Corinthians 13:5 mean?
This statement gives a crucial perspective to all Christians: to think critically about one's own life and walk with Christ. In this passage, Paul wrote that the Corinthians sought proof that Christ was speaking through him as an apostle (2 Corinthians 13:3). Now he instructs them to examine themselves, instead. Are they truly in the faith? Not only does biblical faith involve cautious skepticism (Acts 17:11; 1 John 4:1), it also means being honest and careful about looking into our own lives (1 Corinthians 13:10; Hebrews 4:13). That's not an invitation to doubt (Ephesians 3:14–19), but to honesty (Galatians 6:4–5).Given that this letter was meant for a broad audience—though directed to a particular church—part of the meaning here is a question of salvation. To examine one's self, spiritually, includes an honest look at whether one is truly a believer in Jesus. Along with that, it calls Christians to examine the details and results of their faith, to see if it's according to the truth. It would involve scrutinizing one's own conduct to see how—or if—they follow through on the will of God for their lives.
In short, Paul is asking them to see if Christ is truly in them. Do they still believe what they believed when Paul first introduced them to Jesus? Or will they find that their trust has been in someone or something else?
Paul assumes the answer will be positive. In part, he likely means that understanding Christ's presence within them will motivate the Corinthians to shun sin. It also implies their honest answer—that Christ is in them—will show that Christ is also in Paul and speaking through him (2 Corinthians 13:6). This is true because Paul is the one who introduced them to Christ in the first place. They cannot reject Paul as a false apostle unless they also reject Christ as false in themselves, as well.