Having read Henry V, I think I can sum up the plot as follows: the French insult King Harry, Harry get royally ticked-off, goes to kick some French butt, and comes home with a damned saucy wife. Right now I enjoy any play that shows a contemptuous French government getting smacked down, but this play is not numbered among Shakespeare's heavy-hitters. For one thing, King Harry is not a very interesting character. In fact, I can't stand him - he is a faithless, glorified basher of heads. Shakespeare knows this, that's why he only struts around giving rabble-rousing speeches.
There is a host of other colorful characters in the play (such as Ancient Pistol) but Henry V suffers in comparison with the two parts of Henry IV because of the absence of Falstaff. Falstaff is the most interesting character in the Henriad. By this time, King Harry has treacherously banished Falstaff and he has died of a broken heart. Therefore, there is no cynical commentary in Henry V. If Falstaff had been around, he would have completely undermined King Harry's posturing.
The induring legacy of the play seems to be the films made of it by Olivier and Branagh. Ironically, these are two of the best films made of Shakespeare - partially because the play is so direct and accessible. It is a short, brutal piece about war. King Harry is so good at making speeches, most readers miss Shakespeare's subtle judgement on his central character's hypocrasy.