What does Matthew 7:5 mean?
Jesus has told His audience in direct terms not to judge each other, else they will also be judged (Matthew 7:1). He does not mean that people should have no discernment about sin, even in the lives of other people. Instead, the command forbids playing God (Matthew 7:2). Christians are not to pronounce God's judgment on other sinners while leaving our own lives unexamined or un-judged. We are not qualified to fill God's sinless, righteous shoes. To judge the sin of others while ignoring our own is as absurd as criticizing someone with dust in their eyes, while our own eye is impaled by a stick (Matthew 7:3–4).However, Christ also says we are qualified to help each other remove sin from our lives. To say to a brother or sister "let me help you remove sin from your life" is different from pronouncing God's judgment on them. Of course, Jesus has emphasized that we are not qualified even for that role until we have addressed the obvious sin from our own lives. Otherwise, we become "hypocrites," a term derived from the Greek word for "an actor or pretender."
Once we have worked to remove some sin from our own lives—or at least dealt with egregious sins—we may be able to help remove the sin from another person's life, in humility and service.