From Hume's History of England
Shakespeare also condenses Henry IV and Henry V together, making both parts of Henry IV really about Henry V's journey to maturity -- this time taking a great deal of liberties with the facts, moreso than in Richard II.
Henry IV
As a usurper, Henry IV could never expect much stability in his reign -- an "unruly aristocracy" indeed.
Henry, in his very first parliament, had reason to see the danger attending that station which he had assumed, and the obstacles which he would meet with in governing an unruly aristocracy, always divided by faction, and at present inflamed with the resentments consequent on such recent convulsions. The peers, on their assembling, broke out into violent animosities against each other; forty gauntlets, the pledges of furious battle, were thrown on the floor of the house by noblemen who gave mutual challenges; and “liar” and “traitor” resounded from all quarters. The king had so much authority with these doughty champions, as to prevent all the combats which they threatened; but he was not able to bring them to a proper composure, or to an amicable disposition towards each other.
More religion talk -- he might have had different private principles, but looked to Church support to bolster his reign
While a subject, he [Henry IV] was believed to have strongly imbibed all the principles of his father, the duke of Lancaster, and to have adopted the prejudices which the Lollards inspired against the abuses of the established church: but finding, himself possessed of the throne by so precarious a title, he thought superstition a necessary implement of public authority; and he resolved, by every expedient, to pay court to the clergy. There were hitherto no penal laws enacted against heresy; an indulgence which had proceeded, not from a spirit of toleration in the Romish church, but from the ignorance and simplicity of the people, which had rendered them unfit either for starting or receiving any new or curious doctrines, and which needed not to be restrained by rigorous penalties. But when the learning and genius of Wickliffe had once broken, in some measure, the fetters of prejudice, the ecclesiastics called aloud for the punishment of his disciples; and the king, who was very little scrupulous in his conduct, was easily induced to sacrifice his principles to his interest, and to acquire the favor of the church by that most effectual method, the gratifying of their vengeance against opponents. He engaged the parliament to pass a law for that purpose: it was enacted, that when any heretic, who relapsed, or refused to abjure his opinions, was delivered over to the secular arm by the bishop or his commissaries, he should be committed to the flames by the civil magistrate before the whole people.
He even had to look toward the House of Commons to try to cobble together legitimacy. (This may be too big of a quote to pull, but the history of Parliamentarianism is a pet interest of mine).
During the greater part of this reign, the king was obliged to court popularity; and the house of commons, sensible of their own importance, began to assume powers which had not usually been exercised by their predecessors. In the first year of Henry, they procured a law, that no judge, in concurring with any iniquitous measure, should be excused by pleading the orders of the king, or even the danger of his own life from the menaces of the sovereign. In the second year, they insisted on maintaining the practice of not granting any supply before they received an answer to their petitions, which was a tacit manner of bargaining with the prince. In the fifth year, they desired the king to remove from his household four persons who had displeased them, among whom was his own confessor, and Henry, though he told them that he knew of no offence which these men had committed, yet, in order to gratify them, complied with their request. In the sixth year, they voted the king supplies, but appointed treasurers of their own, to see the money disbursed for the purposes intended, and required them to deliver in their accounts to the house. In the eighth year, they proposed, for the regulation of the government and household, thirty important articles, which were all agreed to; and they even obliged all the members of council, all the judges, and all the officers of the household, to swear to the observance of them. The abridger of the records remarks the unusual liberties taken by the speaker and the house during this period. But the great authority of the commons was but a temporary advantage, arising from the present situation. In a subsequent parliament, when the speaker made his customary application to the throne for liberty of speech, the king, having now overcome all his domestic difficulties, plainly told him that he would have no novelties introduced, and would enjoy his prerogatives. But on the whole, the limitations of the government seem to have been more sensibly felt, and more carefully maintained, by Henry than by any of his predecessors.
Henry V
He drastically out-conquered what could be absorbed. The texture of legitimacy in these times is well illustrated in this passage.
Such was the tenor of this famous treaty; a treaty which, as nothing but the most violent animosity could dictate it, so nothing but the power of the sword could carry into execution. It is hard to say whether its consequences, had it taken effect, would have proved more pernicious to England or to France. It must have reduced the former kingdom to the rank of a province: it would have entirely disjointed the succession of the latter, and have brought on the destruction of every descendant of the royal family; as the houses of Orleans, Anjou, Alençon, Brittany, Bourbon, and of Burgundy itself, whose titles were preferable to that of the English princes, would on that account have been exposed to perpetual jealousy and persecution from the sovereign. There was even a palpable deficiency in Henry’s claim, which no art could palliate. For, besides the insuperable objections to which Edward III.‘s pretensions were exposed, he was not heir to that monarch: if female succession were admitted, the right had devolved on the house of Mortimer: allowing that Richard II. was a tyrant, and that Henry IV.‘s merits in deposing him were so great towards the English, as to justify that nation in placing him on the throne, Richard had nowise offended France, and his rival had merited nothing of that kingdom: it could not possibly be pretended, that the crown of France was become an appendage to that of England; and that a prince, who by any means got possession of the latter, was, without further question, entitled to the former. So that, on the whole, it must be allowed that Henry’s claim to France was, if possible, still more unintelligible than the title by which his father had mounted the throne of England.
Parliament did not want to fully financially support this project.
The authority which naturally attends success, procured from the English parliament a subsidy of a fifteenth; but, if we may judge by the scantiness of the supply, the nation was nowise sanguine on their king’s victories; and in proportion as the prospect of their union with France became nearer, they began to open their eyes, and to see the dangerous consequences with which that event must necessarily be attended. It was fortunate for Henry that he had other resources, besides pecuniary supplies from his native subjects.