If we trace Henry V's trajectory over the course of all three Henry plays, then we can see how his is a classic "Rebirth" story.
Wild Prince Hal is portrayed as a reckless teenager. (Henry IV Part 1)
Booker says that, in the "falling stage," the hero is "underdeveloped" and in the shadow of something "dark" that may "spring entirely from within the hero's own personality." In other words, Hal behaves like a hoodlum because he wants to, not simply because he's been spending a lot of time with Falstaff.
Hal becomes King Henry V. (Henry IV Part 2)
In this stage, the "dark" power seems to have receded. Henry has shrugged off the wild days of his youth and begins to act more like a responsible monarch.
The Dauphin of France insults Henry. (Henry V)
Just when Henry was beginning to feel like a grown-up, the Dauphin sends him an insulting gift (a chest of tennis balls) and suggests that he hasn't changed at all and is still the same old reckless boy.
Henry and his troops prepare for defeat at Agincourt. (Henry V)
On the eve of the battle, the French troops outnumber the English and Henry's army seems to have given up all hope. Henry feels as isolated as ever and delivers a lengthy speech about the difficulties of kingship.
Success at Agincourt – Henry marries Catherine.
Booker says that in this stage, the protagonist is saved by a child or a woman. After defeating the French, Henry is named heir apparent of France and is wed to Catherine. Does she save Henry, though? Maybe. We could argue that the union restores Henry's sense of honor and fulfills Henry's desire to unite both realms.