Is Henry V a good king in Shakespeare's 'Henry V '?

Your answer should be nuanced: yes and no.
According to the chorus, Henry is "a mirror of all Christian kings". He is a heroic man who leads his men with rhetorical energy, camaraderie and charisma. He successfully leads his men into the apparently impossible battle situation of Agincourt and dedicates his victory not to himself but to God. He is shown to deal fairly with his friends (see his treatment of Bardolph). Henry is ultimately vindicated, on a political and personal level, at the end of the play by his marriage to Katherine: he turns war into love.
And yet... he can also be considered a monstrously efficient war machine - John Sutherland calls him a 'war criminal'. He orders the preemptive killing of French prisoners of war; rejects with complete callousness his friends, notably Falstaff; is capable of pathological sexual violence. His rejection of Falstaff is particularly important: according to Emma Smith, Falstaff was the most popular character of the period until the closing of the theatres in 1640s. Stage versions which are pro-Henry cut the play's repeated allusions to him (see: Olivier's very patriotic film version).
You should consider when answering this question at greater length:-the use of irony: Gerald Gould, recently returned from France after WW1, gave the first sceptical reading of 'Henry V' in which he argued that the play was a scathing satire of patriotism and jingoism. -the role of the chorus in relation to events: is the chorus an unreliable narrator? See the 'little touch of Harry in the night speech', which informs us that Harry warms the hearts of his troops, but in the next scene Williams, Bates and Court all complain that they think they're going to die and Henry gets in an undignified row with them!