This seems to repeat the 5h commandment but there is a significant difference. The basis of the 5th commandment has root in the authority given and derived from God, but Ephesians has to do with the relationships in the home- parents and children. When he speaks of obedience he also calls those who dictate what must be obeyed as God dictates and requires of them what is to be obeyed.
The Relationship: We are the body of our Lord Jesus Christ chosen from all of eternity and deal with one another as SAINTS of God. In that church there are many relationships and Paul now zeros in on the relationship of parents and children. It is how God gathers His church and serves the gathering of it. God sets this relationship for the SPIRITUAL care and furtherance of His church. Though we are saints we are also sinners! Even as we deal with that in the fellowship of saints it also pertains to parents and children. Children are not "innocent" as we hear so often said today, but sinners, born and conceived in sin and they are to honor mom and dad as weakest means. And as we stand in parent child relationships as sinners it holds true to all other relationships. Parents and children must bow together in obedience as sinners and it is paramount in dealing with the flesh and the old man as we teach our children. If parents miss that they will either be tyrants and dictate or blend in with their children setting aside their parental responsibilities.
Calling: The calling is to obey mom and dad. This is "right" because God says it is! Paul speaks of obedience and honor. When you obey you honor them and when you disobey you dishonor them. The child must know obedience to their parents and beware of belittling childrens "cuteness" when they are naughty. God says LISTEN and God has chosen you as a child to be His child and born of your parents to be who you are as a being and a person here AND in heaven and has placed you under your parents to bring up HIS CHILDREN to His glory! Therefore parents must set policy to legislate and God gives them the right to bring the children up in God' fear and to set rules for that. Parents do that as sinners and make mistakes and children in pointing that out to get the "monkey off their backs" is sinful. Children must therefore be patient and forbearing of these sins. Parents are to bring them up in the fear of the Lord with admonition (teaching them) and nurturing (disciplining) them that they may be brought up to serve the Lord in their capacity. We are to bring up our children to be Christians, citizens of the Kingdom and we often miss this very point! God gives the callings (jobs, money, etc) but the primary calling is teaching them to be a child of God. That is FIRST and foremost! The principles of a sanctified christian life MUST be instilled in them "that they may be furnished: completely equipped to be children of God. Do not provoke (discourage) them to wrath. We often vex or irritate them. Anger bears the opposite result. What provokes them? Proverbs says "train a child in HIS way. There is quite a list of things. Overprotecting them; you cannot swim for them their entire life. Favoritism; breeds hatred and animosity in siblings. Discouraging; we hold the bar to high. We must KNOW the child and train them understanding their abilities and encourage them! We don't allow them to be themselves; we talk AT them and not WITH them and never give opportunity for them to shine and develop. Abuse. Verbal abuse and we demoralize them and they do not dare to do anything. We need to guide, direct, and discipline them and encourage them to be HIS children as they are able and the Lord WILL bless that!
Blessing: Both parents and children may expect God's blessing when these things are done. Children will stand strong and be thankful and parents will see blessings on their feeble efforts. Children.....obey! Parents....do that which is right and not anger that child for this is right! These things do have eternal ramifications!