Why is Paul's gospel language not found in Acts 5-8?
That gospel language is absent from Acts 5–8 because Peter did not preach Paul’s gospel of grace. The language is unique to Paul, who is the apostle of the Gentiles. The verses in 1 Corinthians 15:1–4 state the gospel that must be believed.
Les explains that Peter did not preach Paul’s gospel of grace, so that specific language is not found in Acts 5–8. He notes that the difference between Peter’s preaching and Paul’s was recognized, and that Paul’s gospel is stated plainly in 1 Corinthians 15:1–4. Les says this language is unique to Paul because Paul is the apostle of the Gentiles, so readers should be aware it does not appear in those early Acts chapters.