M., I am sorry that you are having such a rough time with your 5 yo. I read some of your previous messages and can see the frustration that you're experiencing. Yes, it is good to get information from other mother's experiencing adhd questions but what will be most beneficial is getting a professional opinion. ADHD is too complex to diagnose over the internet.
You could start with her pediatrician who will refer you to a specialist. Or you can start with a clinic specializing in child psychiatry. Another Mamasource mom took her child to Cascadia Behavioral Clinic in Ptld for diagnosis and help with her challenging child. It charges you on a sliding fee scale. There will be a similar state supported clinic in your area.
From reading a previous message from you I'm wondering if you and your daughter have developed a relationship mired in power struggles. You say that you've handled misbehaviour by taking away toys and priveleges to the point that she has nothing left. Wow! If I were your daughter I would be so angry that I'd strike out at everyone. I understand why you would use the "taking away" approach. Removing toys and privileges is a time honored and effective parenting technique. But it's not working for you. One reason that it may not be working is that it sounds like that is your main focus.
I believe, along with most experts, that this sort of discipline needs to be balanced with twice as much, or more, of positive reinforcement. Catch the child doing something right and reward them with praise and any other small rewards that works. My 6 yo granddaughter is currently excited about star stickers. She pastes them onto a plain piece of paper. She also fights with her 3 yo brother and so I was surprised last week when she asked for 8 stars so that she could give her brother 5 of them. They're inexpensive, too.
If your daughter is feeling that she has no control over anything and this is likely, letting her choose how many stickers she gets is a simple way to give her just a little bit of sense of power. Another way is to give her choices. "do you want to have a banana or an apple for snack?"
I think it's important to give a child lots of loving attention even when they are misbehaving. Or I should say especially when they're misbehaving. Everyone of us function at our best when we believe that we are the best. If we hear mostly what a bad person we are we get discouraged and either give up or fight in anger.
Acknowledging her anger and giving her an alternative way to hurting her baby sister will help her learn how to manage her anger. "It is OK to be angry. It is not OK pull your sister's arm! Here is a pillow to hit." or throw. Or suggest that when you see that she's getting out of control that she run back and forth down the hall 5 times. Say or do something funny to distract her. Instead of a time out, after she's thrown that toy across the room have a cool down corner before she's out of control, away from the noise of the rest of the house, with soft pillows and books or quiet toys for her to play with.
I'm guessing that you're feeling quite discouraged and perhaps feel that you are a "bad" mother which makes it hard for you to be calm and detached when your daughter is misbehaving. You are doing the very best that you can with what you know now. The key to success is to get more information, like going to a specialist to learn what is going on with your daughter and how to handle it, and to get more positive attention for yourself so that you feel good about yourself.
You might ask how you can give your daughter positive attention when she's misbehaving all of the time. I'd suggest set up specific times to do positive things. For example, always read to her before going to bed. I adopted my daughter when she was 6 and even tho we struggled with each other throughout the evening I always sat beside her once she was in bed and read to her once she calmed down. She was often upset and acting out at bedtime. She was my only child and so I could sit quietly for a long time. And it was while doing this that she would talk with me about the things that were upsetting her. I did this every night.
You might have to do something else. An idea is to find a time when you can devote 15-30 minutes of time each day or a even just acouple of times a week, with just her. Helpful things are to read together, rock and talk, take a walk, go to the playground. Whatever you can find to do that is satisfying to both of you. It may take trying out several different things or doing the same thing several times to find just the right fit. Since you report that she seems hyper an active activity might work best at first.
I've noticed that a lot of kids don't know how to calm themselves down and so they do appear to be ADHD. And it's no wonder they can't slow down. We live in a fast paced world and many adults can't slow down. You have 3 children. You probably don't have much opportunity to just sit and be quiet yourself. Spending that time focused just on your daughter will be helpful for quieting yourself too. It will take time to develop a peaceful satisfying experience.
YOu're a single parent and so doing this will be especially difficult. Is there a way that you can arrange for someone to help you? My daughter is fortunate is some ways. Her son's father has him a couple of days a week, his other grandmother another day. And while he's gone my daughter spends time alone with her daughter and then I keep the daughter and she has time alone for herself. If you don't have family who can do that for her perhaps you have a friend. When my daughter was young, I had a friend who took her every Friday evening. And other friends who would watch her for an hour or two here and there.
Scheduling time for yourself and time alone with each child can be very difficult but it's worth it when you find that everyone is happier as a result.
I also noticed that you have a 5 mos old baby. I suspect that some, if not a lot, of your 5 yo acting out is in response to the new baby. Have you explored ways to help the older children deal with that?
My heart goes out to you. I know that you have an extremely difficult job raising 3 children as a single mom. I don't think that I could've handled more than the one that I had. The most important thing that you can do is find ways to take care of yourself so that you have the energy and patience to deal with these very active kids.