I think this sounds about like what I would expect as normal behavior from a five year old. They love animals, and don’t want to leave them alone. My SD6 has come a long way with my dogs, but when she was 5, she definitely didn’t understand as well that they don’t like being hugged tightly, etc. It took a lot of work. She craved (and still craves) attention, but when we were first working through our transition stage, I definitely took her hurt for open defiance. She would look at me with this sour look on her face and I would think “you’re purposely sassing me!” I would try to correct her “sassing” and it would blow up in my face every time.

In actuality, I have learned that this is the very face she makes when she feels rejected. It has taken us a long time, but we communicate so much better now. I definitely still make mistakes with her, but we are better able to talk it out, and I understand that she truly isn’t trying to be mean/hurtful to me. I believe it’s true that people who are hurting hurt others. They feel hurt, so in a way it seems that they are rejecting you before you have the opportunity to reject them. Now if she gives me a sour look (most of the time) I am able to say “hey, you look really upset”. She will often say that she is, and ask for a hug, or she’ll burst into tears. Then we can get to the heart of the matter and sort things out.

I’m not saying all of this is necessarily true for your SD, but from my experience, she may want a good relationship with you (you may be the only mother figure she really has) and she may (rightfully or wrongfully) perceive you as not liking her. Bottom line, stepparenting is hard! It’s definitely not for the weak of stomach!

ETA: Her dad should definitely be correcting her if she's misbehaving. I'm able to correct my SD6 much more easily now because we now have a trusting relationship, whereas that wasn't the case before. This is just another side of things that may help you get to the point where she accepts you as a disciplinarian.

Im repeating what others have said. By your own admission you are new to this situation, so you should really be taking a step back.
Her father should be parenting her, you are the girlfriend, you have only just moved in, you need to be looking at this differently. You get to enjoy this little girl when you want to.

Its quite a weird concept for a child for another random adult to suddenly move in with her dad and be able to tell her off like daddy does, but this woman isnt her mum, isnt a teacher, shes what? Shes not sure.

At this point, in early days you should be concentrating on your relationship with your boyfriend, because ultimately if thats not solid then nothing will come of anything anyway. And when it comes to SD, give it some time, build a relationship with her based on her being a kid and you an adult, do some activities together. Invite her to bake with you sometimes, do some crafts if you fancy it, ask her if you can join in playing with her if you want to. But make it on both of your terms, dont expect her to just suddenly have you walk in and be in a position of family-like relationship without there being anything there.

All five (and even 15yr olds) are like this if given the chance to be. As the man point being pushed here agrees Dad should be doing the parenting, which is correct, I'm going to assume one of two things 1. You are being asked to babysit in Dad's absence (example dad is at work) or 2. Dad is home and doesn't have the same parenting standards you have or is shoving his duties of parenting off on new substitute 'mommy'.

Whether you're 'mother' or not, SD needs to mind and respect you in Dad's absence or you shouldn't be agreeing to babysit. However, if this is indeed going on under Dad's physical watch, you have a bigger problem.