A student asked me recently if Hebrews 1:5 supports the doctrine of the eternal generation of the Son. Here's Hebrews 1:5 from the NET Bible:
For to which of the angels did God ever say, “You are my son! Today I have fathered you”? And in another place he says, “I will be his father and he will be my son.”
Here is the definition of the eternal generation of the Son taken from The Pocket Dictionary of Theological Terms (InterVarsity, 1999):
A phrase used to describe the relationship that exists between the first and second persons of the Trinity. God the Father is said to generate (or “beget”) the Son eternally. In other words, the Son’s identity as Son is defined eternally by his relationship to the Father. Likewise, the Father is eternally the Father by his relationship to the Son. The “generation” of the Son is not to be confused with physical conception or birth, whereby a human father begets a son who did not previously exist. In other words, the eternal generation of the Son does not speak about the origin of the Son but rather seeks to define the relationship of the Son to the Father.
Hebrews 1:5 contains two important Old Testament citations that the author uses to make his point, both of which refer to the sons promised to David as part of the Davidic covenant. The first is from Psalm 2:7. That psalm is often labeled as an enthronement psalm which describes the coronation of the Davidic ruler as God's vicegerent. The Davidic king was God's representative and labeled as his son. The second citation in the verse is from 2 Samuel 7: 14 and accomplishes the same purpose but with a statement from the original mention of the Davidic covenant. So the author to the Hebrews uses these verses to show that Jesus is the ultimate and final fulfillment of the Davidic covenant which promised David that he would always have a son to sit upon his throne. The context of the word "today" in the original setting of Psalm 2 would refer to the coronation of the king, but in Hebrews it most likely points to Jesus' resurrection and exaltation, that is, those events prove without any doubt that Jesus is the ultimate Davidic son. For a comparison to a similar idea, we can turn to Romans 1:4: "who was appointed the Son-of-God-in-power according to the Holy Spirit by the resurrection from the dead, Jesus Christ our Lord." Some people argue incarnation is in view in Hebrews 1:5, which is possible, but because of the connection to Psalm 2:7 and the parallel with Rom 1:4, I don't think that is in view.
So in the end we can assert that Hebrews 1:5 does identify Jesus as the Son of God, but it does so by connecting him to Davidic sonship. It does not speak to the issue of the eternal generation of the Son, and I would argue that it does not refer to incarnation either. I hold to both the incarnation and the eternal generation of the Son, but I argue that Hebrews 1:5 is talking about neither of those issues.