What are some themes?
One major theme of Henry V (and many of Shakespeare's histories) is power. Henry V makes a claim to the French throne and seeks to secure it. While Henry is busy grappling over the French throne, a growing opposition questions Henry's right to the English throne, which Henry rightfully inherited after his dad stole it from Richard II). Through all this political maneuvering, Shakespeare raises important questions about the role of inheritance and succession in the monarchy and what makes a king truly a powerful leader.
I agree with post #2. Shakespeare talks about what makes a king a powerful leader, but also what makes a good leader. The St. Crispin's Day Speech is one of the most powerful speeches in all of Shakespeare's plays and it gives a true sense of the type of leader Henry has become. Henry IV part 1 is a coming of age story about Henry V's development from a teenage ruffian to someone who accepts his place in the kingdom. Henry V goes through what it takes Henry to gain the trust and respect of those he governs.
Another crucial theme is war as a source of human--or at least, in Shakespeare's telling, masculine--virtue. It is significant that Henry proves his worth as a leader through his military exploits. If there has ever been a more powerful evocation of military virtue than Henry's St. Crispen's Day speech, then I am not aware of it. The idea that sacrificing oneself for a cause, and for the man fighting next to you, is the ultimate form of nobility suffuses the entire work, and especially in this scene.