Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Ominous
When your play starts with the death of one of your country's greatest leaders, it's unlikely to be a comedy. When it ends with that leader's less-than-assertive son about to make a spectacularly bad marriage, politically speaking, all our worst suspicions are confirmed. Things don't look so good for Henry. Or for England. We can pretty much see the clouds gathering.
And, of course, along the way there are battles with France, men who die because other men can't stop their petty arguing (we're looking at you Somerset and Richard; R.I.P. the Talbot men), defections to the other side (see ya, Burgundy), and old men whose last breaths sow the seeds of unrest (way to go out with a bang, Mortimer). There are happy plays and then there's this one, which not only teems with darkness in its own right, but sets a grim stage for the play that follows.