Paul wrote the I Corinthians on his 3rd missionary journey in Ephesus in 55 A.D. (Acts 19:1-20, I Corinthians 16:8).
Most of the Corinthians in the church were probably poor or middle class status (I Corinthians 1:26ff suggests this observations). The members consisted of Jews (e.g. Cripus in Act 18:8) and Gentiles (e.g. Justus in Act 18:7).
Paul's letter tells us the spiritual condition of this church. The church members were slow to mature in their Christian faith and conduct. Paul called them "as men of the flesh, and as babes in Christ" (I Corinthians 3:1).
Paul properly learned about the Corinthians' problems from the report of the Chloe's people (I Corinthians 1:11, 5:1). He also could have learned from questions in a letter addressed to him by the Corinthians (cf. 7:1, 8:1, 12:1, 15:1, 16:1).