Henry V falls into the realm of Shakespeare’s history plays. These types of plays were written about real rulers, monarchs, etc. As such, every Elizabethan man and woman would have known a fair deal of information about the title character. Shakespeare’s intention with Henry V, as with many of his histories, is not only to portray the life of Henry that many Elizabethans would have already known about, but also to glorify and praise a popular national hero.
Specifically, the play focuses on Henry as the ideal Elizabethan hero—bold and articulate, yet not without faults. While there are other heroic figures in the play, Shakespeare does not focus on them, but on Henry.
Additionally, Henry V evokes grand images of war and glory in a patriotic way. The play has all the elements of an epic story, moving from the preparation of battle, to its execution, and finally into peace. Phrases like, "But when the blast of war blows in our ears/Then imitate the action of the tiger/Stiffen the sinews, summon up the blood,” in Act III, scene i would have certainly evoked patriotism in the hearts of the audience.
So, in recap, Henry V was written to praise popular English hero and stir up patriotism in the hearts of Elizabethans. Perhaps this was the message Shakespeare intended to send not only to his audience, but to Queen Elizabeth herself. Shakespeare’s intent is ambiguous enough that readers are left to wonder whether Shakespeare praises Henry as an ideal ruler or criticizes him. Of course, Shakespeare’s motives in penning Henry V are multifarious and are certainly not limited to patriotism and the commemoration of a national hero; these are simply some of the more overt themes that Shakespeare intended for his audience and his Queen.
In regards to your comment that Shakespeare may have been sending military advice to Elizabeth, please see the enotes links below, which address this topic in further detail. Since Essex and his men did not achieve a victory in Ireland, but were instead humiliated, it seems unfitting that Shakespeare would have written a play that ends with a triumphant general.
The introduction on eNotes.com for Henry V states that if the passage in the Chorus prior to Act V was meant for the Earl of Essex, it would have been improper (and very unwise) to draw attention to it in a play performed on stage, especially before the Queen. First, Essex's venture to Ireland to "put down a rebellion" there was an utter failure. He returned in September of 1599 in complete disgrace.
Additionally, there is no record that the play was ever produced before 1605, and Elizabeth I died in 1603. It seems unlikely, had it been staged before her death, that the players would draw attention to this failure, or to Essex at all. Though he had once been a favorite of Elizabeth, when he attempted to take the throne from her by force, she had him executed for treason—another reason not to remind the Queen of Essex in any way.
As the Queen's preferred troupe of actors (The Chamberlain's Men), Shakespeare and his fellow actors depended upon the patronage of Elizabeth, and she was not someone to be toyed with. Though she loved England and her subjects, she was harsh when necessary, as was her father, Henry VIII. Not only was Essex executed by her order, but her cousin Mary Queen of Scots was also killed for engaging in treasonous acts. Trying to give advice or reminding Elizabeth of state or personal failures would have been professional suicide at the very least for Shakespeare. My understanding is that the play was never performed in her lifetime.
Note: Shakespeare did, in fact, make mention of items of personal interest to the reigning monarch and/or the audience. Including the supernatural in his plays made them very popular, along with the way he wrote his plays, which were very different from the religious plays (morality and miracle) of the medieval period. While Christopher Marlowe, for example, began experimenting with this new kind of drama, Shakespeare perfected it. In Macbeth, under the reign of James I, Shakespeare wrote about James' ancestor, Banquo, who was a valiant warrior and man of impeachable character. This was a compliment directed from Shakespeare to his king.
I doubt this play was meant to disguise military advice to Queen Elizabeth. More likely, this play was written to uphold a national hero, make the Queen and her subjects proud of their heritage, and to instill a national pride and allegiance to the realm. The English public is not naive enough to believe that their national heros were all wonderfully flawless individuals. The Kings and Queens of Britain have all had their flaws, and Henry V was no exception. However, Shakespeare was careful to disguise any mention of these imperfections within his beautiful language. The winning and losing of the port town of Calais was also a point of contention for Elizabeth I and the English for generations.
Some critics regard this excellent play as being a study of what makes a perfect King (or Queen). Let us not forget that this play is actually the last of three plays that chart the rise of the young, hotblooded Hal to becoming King Henry V. This last play in particular seems to focus on the kind of qualities that you need to possess to be an effective ruler, and we see Henry placed in a number of situations where he has to manipulate and act very ruthlessly in order to achieve his objectives.