Please explain the "test" mentioned in 2 Corinthians 13:5?
Paul’s comments in 2 Corinthians come in the context of a larger discussion:
In v.3 Paul says that the church in Corinth was seeking for a “proof” or test that Paul was truly speaking for Christ as an apostle, to which Paul replied that his audience should apply the same test to themselves. Paul is saying that before they judge him, they should judge themselves. Before they criticize him for not following Christ properly or not speaking for Christ accurately, they should examine themselves to see if they know and live the truth properly.
Paul issued this challenge having already defended himself against numerous accusations levied against him by his critics in the city in the prior chapters of the letter. Paul had patiently explained his teaching and motives against false accusations, so now he turns the tables on the church and asks them to examine their own behaviors and motives to see if they are living in keeping with Christ’s will.
Therefore, Paul's test refers to the question of whether a Christian is operating in the faith, in Christ’s will and according to His word. His critics were those who failed this test since they were carnal Christians operating outside Christ’s will. Since they opposed Paul, in whom Christ spoke, they were failing the test they placed on Paul himself.