Line 5 of the Athanasian Creed begins a a sort of commentary on line 4, which warns against either blending the persons or dividing the essence of the Trinity. Line 5 explains what is meant by not blending the persons.

Lesson from the Creed

For the person of the Father is a distinct person, the person of the Son is another, and that of the Holy Spirit still another.

Athanasian Creed, Line 5

Explanation from Scripture

The three Persons of the Godhead are distinct, but not divided.

As we observed last time, the baptism of Christ gives us a wonderful picture of the distinctness of the three Persons of the Trinity: And when he came up out of the water, immediately he saw the heavens being torn open and the Spirit descending on him like a dove. And a voice came from heaven, “You are my beloved Son; with you I am well pleased” (Mark‬ ‭1‬:‭10‬-‭11‬).

The One who spoke was God the Father. The One who was baptized was God the Son. And the One who descended like a dove was God the Holy Spirit.

In the economy of salvation, the Father, the Son, and the Spirit each exercise distinct functions, but they never work alone.

So the Father foreknows and predestines believers in love, from before the foundation of the world: even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will (Ephesians‬ ‭1‬:‭4‬-‭5‬). But notice that He loves, predestines, and adopts us in and through the Son.

Likewise, the Father sends the Son to secure the salvation of His Church: For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life (John‬ ‭3‬:‭16‬). And He sent Him through the Holy Spirit, for the angel told Mary: The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy—the Son of God (Luke‬ ‭1‬:‭35‬).

The Father draws those He has foreknown and predestined to Himself in the Son: No one can come to me unless the Father who sent me draws him (John‬ ‭6‬:‭44‬). And, having drawn us to Himself in Christ, the Father pours His love into our hearts by the Spirit: God’s love has been poured into our hearts through the Holy Spirit who has been given to us (Romans‬ ‭5‬:‭5‬). ‬‬

The Son has won salvation for us by His life, death, and resurrection: we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he lavished upon us, in all wisdom and insight (Ephesians‬ ‭1‬:‭7‬-‭8‬). And again, it says Jesus was delivered up for our trespasses and raised for our justification (Romans‬ ‭4‬:‭25‬).

The Spirit, meanwhile, applies the grace of God in the work of Christ to us, for it says the God and Father of our Lord Jesus Christ … has blessed us in Christ with every spiritual blessing in the heavenly places (Ephesians‬ ‭1‬:‭3‬). Spiritual means of the Holy Spirit, and so it is the Spirit who applies the grace from heaven to sinners on earth.

Indeed, the Spirit seals us for the day of redemption, assuring our full salvation: you also, when you heard the word of truth, the gospel of your salvation, and believed in him, were sealed with the promised Holy Spirit, who is the guarantee of our inheritance until we acquire possession of it, to the praise of his glory (Ephesians‬ ‭1‬:‭13‬-‭14‬).

From eternity, the Father predestined [us] to be conformed to the image of his Son (Romans 8:29). And it is the Spirit who works in us, to conform us more perfectly to the Son’s likeness: And we all … are being transformed into the same image from one degree of glory to another. For this comes from the Lord who is the Spirit (2 Corinthians‬ ‭3‬:‭18‬). The Spirit does this by planting, cultivating, and maturing the virtues of Christ in us: But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control (Galatians 5:22-23).

Father, Son, and Spirit have saved you—Trinity in unity, as we read in line 3 of the Creed. So we owe each Person of the Godhead equal faith, reverence, worship, love, and praise.