Okay, some kids, while they are IN school ALL day... are behaving great and do whatever is expected & are great students. It is a lot of "work" for a child... .mentally and emotionally.
THEN, when they come home... they simply let it all hang out, because they have pent up stresses or just have to release their yah-yah's after being in school ALL day and "behaving."
Its not that she is trying to be bad/difficult at home... but its just a young child's way or "coping" with their day. At home, is where they 'can' express themselves or by the time they do come home, they just have to release it all. AND, when a child this age comes home... they are OFTEN very tired (but trying not to be) and hungry. This combo makes for a fussy child.
Whenever my daughter comes home... I LET AND ALLOW HER to "deflate. I KNOW she needs to. But I try and navigate her to do it pleasantly. If she is not able to, I make sure she is fed (because she comes home hungry after ALL day at school), and we have a "quiet time" where she CAN re-group, and get back to herself. THIS helps immensely. I don't 'nag' her about what to do/when/how, as soon as she comes home. I LET her deflate and re-group. UNWINDING is what she needs. Like any adult after coming home from an entire hard's day at work.
Girls, are also more emotional, when tired. Sometimes, you need to "allow" a tantrum to come out... otherwise a child gets all pent-up.... like a balloon that can't be filled with anymore air, before it bursts. OR you have her nap. Kids this age still benefit a lot from naps. My daughter was in Kinder at 5 years old as well...and in Kinder they would have a nap time. Or my girl napped when she got home. She still took naps until 1st grade. It helped her a lot. She'd be so tired afterschool.
Sometimes too, when my daughter is like that, I just don't say anything, but I hold her in my lap, and hug her and not "lecture" her and she calms down... and bonds with me and feels better.
It is about navigating their "moods" too... instead of "stopping" their moments of in-ability to cope with certain outbursts. So in this case, punishments do not work. And instead, teaching them 'how' to manage themselves when they don't feel good or are just plain grumpy.
A great book series is: "Your 5 Year old", "Your 6 Year Old" etc. which you can get from www.amazon.com Its a series about each age-juncture and what the child is going through. Although written years ago, it is still very pertinent.
Another great book is: "How to talk so kids will listen, and listen so kids will talk" which you can also get at Amazon or any bookstore.
All the best,
Susan