DD was 3.5, so obviously I don't think it's too young, though I am a slack lazy parent.
I think there are two things. One, do you think they'll be scared? That's something only you will know about your children, and IMO smaller children won't be scared in the way a slightly older one will, because their grasp of it is so much less sophisticated. But if your five year old is imaginative, it might be too much.
Two, do you mind if they don't get every nuance? Personally, I couldn't give a shit about this. I love rewatching and re-reading things. It's the best. My grandparents took me to see Shakespeare at a very young age, and I grew up absolutely adoring Shakespeare and being fascinated by his work. Did I understand everything about The Tempest when I saw it first? Hell no. And I'm bright enough to admit I still don't.
I don't personally think J K Rowling is quite in Shakespeare's league. I can't begin to imagine how a story could be 'spoilt' by seeing it early on. I believe stories just become richer and more enjoyable when we encounter them at different stages.
So I'd say, if you're fairly sure your children won't be upset or scared, then go for it! Just let it wash over them, and then let them watch it again, lots of times, as they get older.