Five year old throws tantrums when in public, usually she’s frustrated at not getting what she wants. Well, I handle tantrums no matter where I am. You don’t be an inconsistent parent. It’s not like you’re one parent at home and you’re a different when you’re out . You must be consistent. The only reason why she’s tantruming at 5 years old is because she knows eventually she might win, because you’re obviously embarrassed when you’re in public. I would recommend working on your leadership skills