It seems the word "we" sometimes refers just to the apostles (eg verse 12-13). Other times it refers to everyone (eg verse 21). However it is often ambiguous (eg verse 14, 20).
This passage is subtle in its construction and (typically) great care with which Paul selects his words.
The pronouns in 1 Cor 5:11-21 fall into two categories:
- those that are some variant of "all" which clearly implies all people
- Us/we in contradistinction to your/yourselves.
Let me be more specific:
- V11 Therefore, since we know what it means to fear the Lord, we try to persuade men. What we are is clear to God, and I hope it is clear to your conscience as well. Note the "we" vs "you" here; therefore, Paul is referring to himself and his associates in distinction from the Corinthian church members.
- V12 We are not commending ourselves to you again. Instead, we are giving you an occasion to be proud of us, so that you can answer those who take pride in appearances rather than in the heart. Same as above.
- V13 If we are out of our mind, it is for God; if we are of sound mind, it is for you. Same as above.
- V14 For Christ’s love compels us, because we are convinced that One died for all, therefore all died. By extension to above, Paul and his fellow-teachers is the "us" but "all" refers to all people, including the Corinthians.
- V15 And He died for all, that those who live should no longer live for themselves, but for Him who died for them and was raised again. "All" means all people.
- V16 So from now on we regard no one according to the flesh. Although we once regarded Christ in this way, we do so no longer. Paul says "we" meaning himself and companions and hints at the way he approaches his ministry.
- V17 Therefore if anyone is in Christ, he is a new creation. The old has passed away. Behold, the new has come! "Anyone" includes all people.
- V18 All this is from God, who reconciled us to Himself through Christ and gave us the ministry of reconciliation: See V19 below.
- V19 that God was reconciling the world to Himself in Christ, not counting men’s trespasses against them. And He has committed to us the message of reconciliation. Paul and his fellow apostles feel the divine calling to engage in the ministry of reconciliation. When the Corinthians are fully converted, they might also be involved in reconciliation ministry as Paul asked them to imitate him as he imitated Christ (1 Cor 11:1, Eph 5:1)
- V20 Therefore we are ambassadors for Christ, as though God were making His appeal through us. We implore you on behalf of Christ: Be reconciled to God. This is a continuation of the above verse.
- V21 God made Him who knew no sin to be sin on our behalf, so that in Him we might become the righteousness of God. This is the trickiest verse as "our" appears to include more than just Paul and his fellow-teachers.
Thus, with the possible exception of V21,
- "we/us" represents Paul and his associates;
- "you" represents the Corinthian church members
- "all" means all people.
What shall we decide for V21? For consistency we might say the same as the other verses or make an exception. However, Paul appears in this passage to be teaching by example - what applies to me would apply to you if you answer the calling of God.
Thus, we might be able to use the above classification and be consistent.