What is meant by adopted sons of God in Ephesians 1:5. I don't find the term anywhere else on the Bible.
This verse is best taken in context, because the verses cut off part of the sentence as we would understand it in English. Note that I prefer the Holman Christian Standard Bible over the King James translation. However, I'm including verses 4-6 KJV here for reference:
Ephesians 1:4-6 King James Version (KJV)
(4) According as He hath chosen us in Him before the foundation of the world, that we should be holy and without blame before Him in love: (5) Having predestinated us unto the adoption of children by Jesus Christ to Himself, according to the good pleasure of His will, (6) To the praise of the glory of His grace, wherein He hath made us accepted in the beloved.
This refers to God's acceptance of people, as His children, who have repented of their sins and declared Jesus Christ as their Lord and Savior, and this not the only place the Bible refers to believers of the Gospels as sons and daughters of God. Some further references, from the Holman Christian Standard Bible translation:
John 1:12 "But to all who did receive Him, He gave them the right to be children of God, to those who believe in His name,"
Ephesians 5:1 "Therefore, be imitators of God, as dearly loved children."
Philippians 2:15 "so that you may be blameless and pure, children of God who are faultless in a crooked and perverted generation, among whom you shine like stars in the world."
Note that all of these passages appear in the New Testament, primarily because the event that makes every person potentially a child of God is Jesus' sacrifice, which is, by and large, the basis for the New Testament.
Note that the Bible states God gave his only "begotten" son as a sacrifice for all of our sins. He has no other son who is birthed directly from Himself, but figuratively, by way of recognizing the sacrifice, and honoring it, we all can become His adopted children.
The whole Bible is about God's choosing Hebrews as His people and making Covenant with them. Gentiles are separated from God in the natural sense until we are "adopted in" or Grafted in to the Vine.(Jesus). We have the right to be sons of God when we accept the sacrifice of Jesus. Christians often have the mistaken idea that somehow God has changed His mind on the Jews and have switched to the Christians for His "people". Not true! The Jews will be saved in the Last Days as in Zech 12:10 and Zech 13:6. The whole book of Zechariah tells about the Jews relationship with God. Antisemitic remarks from Christians mean you literally hate your brothers. We joined their family, not the other way around.