Remember that one of the reasons you are finding it hard to deal is because you are tired, emotional and your hormones are all over the place. Be kind to yourself - we all get driven insane by our children :)
We also tend to have far, far more patience, sympathy and tolerance for our friends kids, so imagine a friend has told you this story. What would you advise her to do; I imagine you would feel quite a lot of sympathy for both mum and child, so remember this as you find your way with DD.
Do you have any books for her on being a big sister? Some are very good as they give the negatives and the positives. It's hard being a big sister, as my own DD1 keeps finding out :)
She is hurt and unhappy so is striving to make you feel the same pain - this is why she lashes out verbally. When she does let her know you understand; tell her something like 'wow you are really mad at me just now. I know you are feeling very upset.' Buy her some puppets and give her permission to play with them as she wants (hopefully short of destroying them!) My DD1 used to role play a monster eating her baby sister - lots of wishful thinking going on there :) I never intervened; she needed to be allowed to express the very strong wish her sister had never arrived! Tell her you miss your special time together - my DD really appreciates it when I too acknowledge that we have lost special time together; it lets her know that time was important to me too.
Involve her in the baby if you can trust her. Now you are expressing maybe she would like to feed the baby? Tell her how proud you are of her for helping dress him, feed him, fold his laundry. Have a reward chart and let her pick the reward - an outing with you, dress up, a dolls tea party with you and so on.
Acknowledge that her fears that there is someone in the house are true - it's her brother! Help her close doors that you can agree can be closed without isolating DS when you need to listen for him. Log onto amazon with her and choose one of those roll up children's beds and put it on the floor by your bed and give her absolute permission that she is always welcome to come to your room to sleep if she needs to. It will be hard but it will reassure her she is still wanted and loved. After all she is only 5 and emotionally she will struggle to understand why the baby can be with you at night and she cannot.
At the same time be consistent and strict with her naughty behaviour. Decide what is not acceptable and focus on 1-2 things and apply time out - or better still, time in - for these things. Don't try to tackle every thing at once. Just look at what is most unacceptable to you. Explain to your parents she is stuggling to adapt to the changes in the family and elicit their support to do things your way.
Finally get her some daddy time too and take yourself off for a soak in the bath and a nap. You'll feel much better for it too. Good luck.