Q: What is the reason annexed in the fifth commandment?
A: The reason annexed in the fifth commandment is a promise of long life and prosperity (as far as it shall serve for God's glory and their own good) to all such as keep this commandment.
Deuteronomy 5:16 Honor your father and your mother, as the LORD your God commanded you, that your days may be long, and that it may go well with you in the land the LORD your God is giving you.
When God gave this command and promise, he gave it to God's people as they were expressed in the nation of Israel, about to go into and live in a land given specifically to them, the Promise Land. The promise of a long and prosperous life in the Promise Land was contingent upon the Israelites keeping God's law, here in particular, to obey and honor parents (and all authority figures). Now, of course, God's people are not limited to one nation and one geographic location, but that does not mean the promise is null and void.
It is important that we understand this is not a magic formula to a long and healthy life. As the catechism points out, these promises are not only contingent on our obedience, but also upon what God deems will bring him the most glory and do us the most good. These two things, God's glory and God's good works towards his people, always take precedence over everything else. And yet, the promises that come with keeping the fifth commandment are good, "common sense" promises. Peace, prosperity, and even longer life are more likely if we listen to the sage advice of our parents and elders, if we submit to the governing authority as far as we can without disobeying God, and if we love one another and serve one another well.