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Or you can do it in more elegant fashion by using setter function on health variable.

var health = 100 setget set_health

...

func set_health(value):
  health = value
  if value <= 0:
    die()
...

func on_area_entered(area):
  self.health -= 5. # It's very important to write self.health instead of health if you use setter function
...

func die():
  $death_timer.start()
  $AnimationPlayer.play("death")