The first thing I wanted to reply to was your comment that Shyliegh won't babysit the younger ones. She is 16 years old and was not the one that decided to have four young children. While I completely agree that watching the younger ones is family responsibility, it absolutely should NOT fall on her shoulders. If you need to do a quick errand, she should want to help, but if she is "babysitting" she should be rewarded for it. My mother had my half-brother when I was 13, and she did an excellent job of not expecting my sister and I to "babysit." It actually made us WANT to help and never made us feel like the family's caretaker. However, if she agrees to babysit (and yes, I believe you should always ask her), then she should honor her commitment.
In my opinion, babysitting siblings does not fall under the responsibilities of an older child.
As far as the other children go, I agree with other moms in that the older children should be kept away from the babies! Some of your comments actually make me concerned for their safety! They should NEVER be left alone with the babies.
I have a 6 & 3 year old and have had the same problem, but less violent and more with bickering over toys & such. I would hold the 5-yr old accountable for all her actions. Do time-outs work? She should have to sit out for 5 mins (within your eyesight) and think about her behavior. Then she needs to explain to YOU why she was in time-out. Then she needs to apologize to her sibling for her behavior. Every single time. I'm guessing she's just jealous? Maybe she could use a little one-on-one time with Mom, but not sure how you'll manage that one! Haha!
Most importantly, make your rules and be consistent. Violence towards siblings should not be tolerated at all.
Wishing you the best of luck! And happy children!