Chapter 5 begins what is commonly called the Sermon on The Mount. Over the next few chapters we hear Jesus basic stance on many of the religious issues of the day. To the Jewish people this would be considered Jesus' midrash, or his interpretation of the scriptures. To the casual reader these might not seem like they are controversial. Part of that is because these passages have woven their way into the fabric of our American society so deeply they seem common.
In Jesus' day these statements were extremely controversial as they were an interpretation of the law which was not part of the common practice. There were people talking about how they had never done it like this before, and how we must we remember the way things have been done around here. But Jesus is directly challenging that. He keeps saying, you have heard it said, then he will tell a new truth. This was exciting some people while it was make some very agitated.
It is a dangerous game when we think we have figured out all the truths about God, and how God works. Jesus could speak with great authority because he is God. You and I are only growing in relationship with God, but not God. The way things were, and the way things are, might not be the way things God wants them to be. We must be open and willing to follow when God says you have heard it said.