"For unto which of the angels said he at any time, 'Thou art my Son, this day have I begotten thee?' And again, 'I will be to him a Father and he shall be to me a Son?' And again, when he bringeth in the first begotten into the world, he saith, 'And let all the angels of God worship him.' Of the angels he saith, 'Who maketh his angels spirits, and his ministers a flame of fire.'"
This series of verses in the first chapter of Hebrews references the Old testament several times. In order to understand these verses, it is best to look at each OT reference (in its own context) and see how the author of this epistle is using it here to uphold the deity and supremacy of Christ. The author starts out asking his reader the rhetorical question: "For unto which of the angels said He at any time 'Thou art my Son, this day have I begotten thee?'" This is only the first part of verse five, the verse goes on as the author asks a second question, but we will pause here and look at the Old Testament reference he utilizes. The phrase "Thou art my Son, this day have I begotten thee" appears in Psalm 2:7, the context is found in vv. 6-8: "Yet have I set my king upon my holy hill of Zion. I will declare the decree: Thou art my Son, this day have I begotten thee. Ask of me, and I shall give thee the heathen for thine inheritance, and the uttermost parts of the earth." (Psalm 2:6-8 bold emphasis mine). This psalm is a messianic Psalm declaring the sovereign rule of the Lord in spite of the world's rejection of Him. Verses 6-8 show the Lord receiving all the earth for His inheritance, not just Israel, but the gentile nations too. Christ's sonship is on full display as God the Father Himself says "Thou art my Son..." So we return to Hebrews. The author quoting Psalm 2:7 asks which of the angels did God ever say that they were His Son. Not one of the angels could ever say that they were the Son of God. Jesus Christ is God's Son, not by adoption, but His begotten Son, the only begotten of the Father.
The second Old Testament verse that is referenced here in verse five is 2 Samuel 7:14: "I will be his Father and he shall be my son. If he commit iniquity, I will chasten him with the rod of men, and with the stripes of the children of men." The surrounding context of this verse is the foundation of the Davidic covenant. The Lord has promised King David that the throne of his kingdom would be established forever, that David's seed would be set up and there would always be someone from the line of David ruling from Jerusalem. The phrase that the apostle emphasizes here in Hebrews is the first part, "I will be his Father and he shall be my son." This is where the Lord is referring to both Solomon and Christ, the rest of the verse obviously does not apply to Christ.
In verse six, the apostle quotes a verse out of Deuteronomy 32:43 but not out of the original Hebrew manuscripts; the author of Hebrews quotes out of the Septuagint, which reads: "Rejoice, ye heavens, with him, and let all the angels of God worship him; rejoice ye Gentiles, with his people, and let all the sons of God strengthen themselves in him; for he will avenge the blood of his sons, and he will render vengeance, and recompense justice to his enemies, and will reward them that hate him; and the Lord shall purge the land of his people." The original Hebrew is quite different but the apostle reckoned the LXX to be scripture and so he quoted it thus. It's interesting to compare the LXX translation of this verse with an Hebrew-based English version such as the KJV. The KJV translates Deut. 32:43 as: "Rejoice O ye nations, with his people: for he will avenge the blood of his servants, and will render vengeance to his adversaries, and will be merciful unto his land, and to his people." It's amazing how the Holy Spirit uses the Septuagint in the New Testament, and I am thankful that God used the LXX translation of Deut. 32:43 instead of the standard Hebrew.