Dr. Ray Pritchard writes, Romans 5 speaks of justification. Romans 6 is talking about sanctification. Romans 5 explains how God declares people righteous. Romans 6 explains how God makes people righteous. Those distinctions are crucial for you to know. Justification is that act whereby God declares you righteous in his eyes. Sanctification is that act whereby God makes you righteous. But those things are not the same:

Justification happens at the moment you trust Christ and is never repeated.

Sanctification happens moment-by-moment as you surrender your life to the Lord.

Justification delivers from the penalty of sin.

Sanctification delivers from the power of sin.

Justification is an event.

Sanctification is a process.

Justification happens once and only once.

Sanctification is gradual and continuous.

Justification cannot be repeated.

Sanctification must be repeated.

Justification is the work of a moment.

Sanctification is the work of a lifetime.

Justification gives you the merit of Christ.

Sanctification gives you the character of Christ.

These two doctrines are distinct yet inseparably related. Justification leads to sanctification. Those who are truly born again are led of the Spirit into a life of growing holiness. This is the true connection between Romans 5 and 6. Romans 5 describes how we are brought into a right relationship with God while Romans 6 tells of the changed life which must issue from that new relationship with God. So, then, these two chapters are distinct yet joined by a natural progression of thought.