What are some key contributions of new historicism, cultural materialism and feminism to Shakespeare, and where are they represented in Henry V?

This is an interesting and valuable question, since it touches on the issue of the extent to which Shakespeare's plays represent or endorse the old feudal order, or rather, look forward into the modern age. New historicism seeks to understand historical processes through literature and is based on the concept of a symbiosis between literature and history. Henry V is in fact a relevant work to look at in this context.
In dealing with historical events Shakespeare, like any author, is reinterpreting the past in light of the mindset of his own period. England during Elizabeth I's reign was a triumphant nation. It had become a world power with its defeat of the Spanish, and the London literary establishment also had a new awareness of the ability of the English to create a literature rivaling or surpassing that of the Romance languages. This national pride is expressed in Shakespeare's histories, especially Henry V. So in reading or attending a performance of it, we are engaged in the process of understanding, through literature, the history Shakespeare is depicting, but also the history of his own period nearly two hundred years after the battle of Agincourt. The extent to which Shakespeare's view of Henry V's time is accurate is something that we have to discover separately from the process of exposure to his work, however. And our awareness of why Shakespeare has altered or reinterpreted history then leads us to a greater understanding of both the period of the Hundred Years' War and of the Elizabethan era.
The issue of feminism and its relation to the events of Henry V is also worth discussing. Henry's claim to the French throne is depicted as based on Salic Law, which held that women were to be excluded from the direct line of inheritance to a throne. In spite of his flag-waving for his own country, is Shakespeare really endorsing this view? Also, what does his depiction of Katherine, the French princess who is to become Henry's bride, tell us about the status of women at the time? The most memorable scene in which Katherine appears, in my view, is the one in which she is attempting to learn English. Beyond the comical mixing up of words, there is a significance to this scene that transcends the effort to adjust to a new language and culture, and perhaps shows the forward-looking features that appear again and again in Shakespeare's depiction of women, in characters as diverse as Katherine, Juliet, Cordelia, and many others.

In looking at Henry V, a new historicist would be interested in what the text can tell us about Shakespeare's time period through how he portrays the past, and, conversely, how what we know about Shakespeare's time period can help us understand the play. They might look at the portrayal of the French in terms of the relationship between France and England in Shakespeare's day.
A cultural materialist would be interested in the technologies portrayed in the play—for example, in the historical battle of Agincourt, the English archers had a technological advantage over the French. Why did Shakespeare choose not to include this element in his play?
A feminist critic would concern themselves with the gender relationships in the play. What does the scene with Alice and Katherine add to our perspective on the play? Why are women's voices brought in so rarely, and what do they do when they are?