Was the sin in 1 Corinthians 5 a public matter known by the whole Corinthian church?
Yes. Paul states the sin was reported commonly, not done in a corner but openly, and the entire Corinthian congregation knew about it. The immorality involved a man having his father's wife, a matter so grave it was not even named among the Gentiles.
Les teaches that 1 Corinthians chapter 5 is not a pretty chapter and one he would just as soon not have to comment on, but since the teaching is proceeding chapter by chapter, it must be dealt with. He notes that Paul writes to the same congregation he had been dealing with for several months. The phrase “it is reported commonly” means the sin was not being done in a corner but was open, and the whole Corinthian congregation, whether large or small, all knew about him. The sin was fornication: one has his father’s wife—immorality so bad that even the pagan Gentiles would not do it.