Psalms 5, is a passage not about vengeance.
But about facing situations where wickedness appears to have gained victory. As if they were saying: "God is on their side".
Psa 5:4 For thou art not a God that hath pleasure in wickedness: neither shall evil dwell with thee.
David cried for God's presence in his meditation upon such crisis. When one will surely fall either by vengeance or succumb to evil deeds.
David turned to God's mercy and instead of seeking revenge, he prayed for a walk in righteousness of God, in order to deal with his enemies, who are essentially those who rebelled against God.
Psa 5:8 Lead me, O LORD, in thy righteousness because of mine enemies...
Today, many miss this point. Because they use words like these to their defense against those they don't like, those not because they are rebelling against God, but simply because of their differences. Jealousy, imprudence, laziness, etc. are usually the cause of this, and thus their prayers are made void by their sins.
Because David take not vengeance, his resolution is to trust God. Psa 5:11 But let all those that put their trust in thee rejoice...
He is not concerned about himself, but the whole community of the righteous. So while he talked of destruction to the enemies, those who walk God's true path, revealed under His mercy, is not only spared from being cast out, but granted the permission to shout for joy.
Such is a true preacher. A preacher who truly hates sins while preaching to sinners while standing in the house of God with reverence.