What does Mark 2:5 mean?"Faith" here is from the Greek root word pistis. It means to be convicted that something is true. As these men demonstrate, it is not a passive belief, but a trust that inherently drives action. James 2:17 says that "faith by itself, if it does not have works, is dead." That doesn't mean that works are required to have faith. Rather, if works don't naturally result from whatever we're calling "faith," then it's not real, saving faith. The four men live out this faith-in-action when they carry their friend and commit minor property damage to get him to Jesus.
Jesus' response to that faith is calculated. The crowd includes Pharisees and scribes from all over Galilee, Judea, and Jerusalem (Luke 5:17). They know He can heal, but Jesus ups the ante by first healing the man's relationship with God, not his physical ailment. He starts to show us why He really came: not to fix our worldly condition, but to ensure our heavenly one. The Greek root word translated "forgiven" is aphiemi and means "to let go, get rid of, refuse to let it hinder." God has let go of his sins (Psalm 103:12).
Jesus forgives the paralytic of his sins before He is crucified for the man's sins. Like the God-followers of the Old Testament, the man reaps the benefits of a sacrifice that hasn't happened yet. God lives outside of time. Although He works in human history in different ways in different ages, His grace and forgiveness are always based on the moment when Jesus died on the cross. When Hebrews 11:1 says "faith is the assurance of things hoped for, the conviction of things not seen," "not seen" can mean things we didn't experience personally or events that haven't happened yet. In the same way, we can have faith that Jesus will return.
Mark says that "when Jesus saw their faith" He spoke to the paralytic. However, it is important to note that the man is not forgiven because of his friends' faith. We don't know why Jesus doesn't declare that all their sins are forgiven. Perhaps because He would only heal one in His impending illustration of authority. We aren't saved by the belief of others, including parents and spouses. We need to accept Christ's forgiveness of our own accord. Even so, whenever we pray for others, whether for physical healing or spiritual forgiveness, we should do so with faith that God can do what we ask and that He will do what is best.