Over many years, I have taught Shakespeare’s great tragedies dozens of times & have been asked this question hundreds of times by students. For the first time, I offer my humble opinion.
#5 Romeo & Juliet
You will find some brilliant passages on the nature of love from a variety of perspectives, but comparatively, this is a fledgling, rambling play.
This is a dark, brooding cautionary tale, but for contemporary audiences, the play’s dramatic impact is hampered by its supernatural elements.
This is probably the most accessible of Shakespeare’s tragedies but it lacks the profundities of his best work. That said, the scheming Iago is amongst the finest of Shakespeare’s creations.
#2 King Lear
This is a brilliant philosophical play, but in parts, such as Lear’s storm sequence, totally incomprehensible, even to a close observer of the play.
This is clearly Shakespeare’s greatest work. Hamlet’s inner struggle, as embodied in his soliloquies and philosophical diatribes, are unparalleled in Western literature.