OK, you seriously need a break on a regular basis...and you need to allow yourself to have that break.
I don't know if you have a hubby/boyfriend/SO/partner working outside the home as the "breadwinner", but if you do, he/she needs to seriously step up and help out at home a little. Hopefully he/she is not working 14 to 16 hours a day, 7 days a week, and would be able and willing to wash a load of dishes, run some laundry, play with kids some and help get them ready for bed. Sometimes just that one little thing makes a huge difference. And days off they can do even more.
It's okay to let them watch TV if it gives you a bit of sanity. If nobody else can watch them without resorting to TV, how do you expect yourself to manage? 1 to 2 hours a day of some Nick Jr. or kid-friendly video won't hurt them. No really, it won't.
If they are able to watch some TV or get engaged in some activity (coloring, playdoh, etc.), that's the time to get something to eat for yourself. Any interruptions are met with, "Sorry, but I am eating right now, you will have to wait." Unless someone is bleeding or has a broken arm or is on fire, they can wait.
You will probably have to do 2 to 3 loads of laundry a day to keep up. You won't have it all done at once, but it won't be out of control either. Paper plates and cups are your friends.
For the older kids, you need a zero-tolerance policy for the problem behaviors. Screaming, fighting, crying (except when really hurt), whining, hitting and smacking earns them time-out in their rooms, separated from each other and everyone else.
Get some bins and other items for organizing toys and making clean-up easier. Then they can help you gather up blocks, Legos, books, etc. and put them where they are supposed to go. Start introducing a schedule and some structure to their day. Make a chart if it helps. Bathe 1 or 2 kids every night so they are getting a bath more than once a week.
Hopefully the 5 yo is going to kindergarten in the fall and the 4 yo can go to preschool. See if the younger ones can go to a Mother's Day Out program 1 or 2 days a week for a few hours and then you could really catch a break. See if there is a teenager in your neighborhood that can do some babysitting or act as a Mother's Helper.
See if you can get a cleaning person to come in every 1 to 2 weeks to get some deep cleaning done.
Your house may never be "perfect" but it should be "good enough" where it doesn't feel so crazy and chaotic.
Once the youngest one is in school full-time, see about going back to work, even if it is just part-time.
Most importantly, don't feel like you have to be Super M. or some kind of martyr to be a good M. to her kids. You don't have to enjoy every single moment with them but not liking any of the time spent with him will begin to make you resentful and they will pick up on that. If Mama's not happy, ain't NOBODY happy. Having some breaks here and there, and making sure they happen no matter what, will help recharge your batteries so you can enjoy your time with them more.
ETA: Read your other post about your husband - while I think he needs to improve his attitude, I would agree with others that have said you don't need your kids in all these activities at this age. If you had 1 or 2 kids, maybe some would be ok, but not when you have 4 kids ages 5 and under. Maybe you need to think about if all these activities are really benefiting them if their house is in chaos and Mommy doesn't enjoy spending time with them and Daddy is too stressed at the end of the day to have much to do with them either. They need happy parents and a happy home more than enrichment classes right now.