It sounds so tough, my heart goes out to you.
But I don’t think leaving her to cry it out is the answer either, particularly in these circumstances. Her dad has abandoned her. She’s testing you to see if you’ll abandon her too. She’s unlikely to be aware of that but that’s what it boils down to.
At 5 she should be old enough for a sensible chat about what she is thinking when she’s screaming like that, and that it’s really got to stop. But also let her know in no uncertain terms that you won’t be leaving. This needs saying.
What I’d probably do is establish a firm bedtime routine - bath, pjs, teeth, one book, hug. And then no talking! But agree this with her. If a reward chart is helpful, use one, but be sure she understands what is required. It’s more likely to succeed if she has a sense of contributing to the solution.
Sit in the doorway with your book or tablet and wait. It’s going to take a bit of time, but it won’t be forever.
It’s really not helpful to think about her controlling you, in an equivalent way to domestic abuse. I sympathise with the feeling, but thinking like that isn’t going to help you. It’s better to see her a vulnerable girl trying to rebuild her foundations.
Let the house be a tip for a while. We can hire cleaners to sort a physical mess but it isn’t as simple to clean up emotional messes or build relationships.