I have been reading First and Second Corinthians. In 1 Cor. 5, the man whom was in the incestous relationship with his stepmother was sentenced to death as judgment for his sins. But in 2 Cor. 2, how is this same man then reconciled back to the church?
The connection you assumed between the person mentioned in 1 Corinthians 5 and the person mentioned in 2 Corinthians 2 is not supported by the text. There is no reason to assume that the person described in the first passage is the same person being discussed in the second passage. In fact, internal references in both letters would argue otherwise.
First, we know that Paul wrote at least three (and likely four) letters to the church in Corinth, based on Paul’s own references to his writings. Secondly, Paul made at least three visits to the city, including at least one journey not recorded in Acts, so there were other events in Paul’s experiences with this church that we do not have recorded in Scripture. In 1 Corinthians 5:9 Paul references an earlier letter he wrote, and in 2 Corinthians 12:14 he referred to his next visit as his “third”.
Therefore, the events Paul mentions in 2 Cor. 2 are not necessarily the same events Paul wrote about in 1 Cor. 5. Given Scripture’s incomplete record of Paul’s dealings with the church, we must allow for the possibility that 2 Cor. 2 is referring to other events outside the record of Scripture.
Moreover, Paul's descriptions of the two circumstances in 1Cor. 5 and 2 Cor. 2 simply do not match. In 1 Corinthians the man's offense was named specifically by Paul (1 Cor 5:1), while in 2 Corinthians Paul refrained from mentioning his offense in order to protect his identity (2 Cor 2:5). In 1 Corinthians, Paul judged the man from a distance, but in 2 Corinthians, the offender was judged by “the majority” (2 Cor 2:6). In 1 Corinthians, Satan carried out the judgment, but in 2 Corinthians the majority carried out the punishment. In 1 Corinthians the offender’s punishment was suffering the end of his life (i.e., the “destruction” of his flesh for the saving of his soul), while in 2 Corinthians the man was ultimately restored and received by the body.
Given these differences and our inability to know for sure which prior letter was Paul referring to in 2 Cor. 2, the safest interpretation is that the man in 1 Cor. 5 did something very serious and was punished with loss of life, while a different man mentioned in 2 Cor. 2 did something less offensive and was ultimately restored.