All through the Old Testament the priestly mission moves in the opposite direction of the prophetic mission. Prophets move in mission from God to man. They reveal. They proclaim. The movement is from up to down. Priests minister from man toward God. They lead in repentance. They offer sacrifices. They enable worship. The movement is from down to up. Something must be accomplished in the ministry of the priest to open up a way to reach a holy God.
This is what our writer means with those very precise words, "...appointed to act on behalf of men," and "...in relation to God"(5:1). Men and women like us can't get to God. God would be nothing but an unbearable threat to the likes of us.
The solution to our dilemma is some kind of sin remedy. All through the Old Testament there must be some form of payment for sin - some sort of substitution. Our writer wraps up verse one with the divine plan - "For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins."
Our New Testament writer feels we need the repeated Old Testament lesson. All priests are useless in their help to the people apart from the offering of sacrifices. Priests offering mere sympathy are an empty hope. Lectures about divine law and morality won't change the sinner's relation to God. Worship offered apart from the sacrificial shed blood will be offensive to a holy God.