Is Paul asking for the man's soul and spirit to be destroyed in 1 Corinthians 5?
No, Paul is not asking for the man's soul and spirit to be destroyed. He delivers the man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord Jesus. The soul and spirit are distinct from the flesh, and the man is a believer.
Les explains that when the church at Corinth was gathered together with Paul's spirit and the power of the Lord Jesus Christ, the instruction was to deliver such a one unto Satan for the destruction of the flesh. Les emphasizes that the flesh and the soul and spirit are not the same. Paul is not crying or demanding the destruction of this man's soul and spirit as a believer. The man is a believer, or they wouldn't address him as such in the Corinthian letter. They could turn him over to Satan to destroy his physical life or his flesh. Satan can only go as far as God permits, as seen with Job. Les says Paul is saying that if this couple will not clean up their act and come away from their open sin, then turn them over to Satan to destroy the flesh, to take their lives physically, lest they bring reproach to Christ's name. This does not mean they will be annihilated spiritually. The verse continues that the spirit may be saved in the day of the Lord Jesus. Les notes it is hard for many to comprehend that people living in this kind of sinful condition are still saved, but they will not get away with it.