OP I feel you, I also have 4 DC, 5th on the way and eldest is 8, DP currently doesn’t live with us. It’s a shit show half the time and feels like I’m never on top of everything and always dropping balls, I get very stressed about it at times but then I just think half of this stuff doesn’t matter, like pp’s have said, prioritise and forget the rest for now - as long as your kids are happy and healthy that’s okay.
I have ADHD, is this something you’ve ever thought about for yourself? Even if not, look into the coping mechanisms for it - it might help to organise your brain a bit.
practicality wise, number one rule is don’t put anything off, ever. Do it straight away. Kid comes home with a form for a trip? Sign it straight away and put it back in their bag. A job needs doing in the house? Do it straight away, as soon as I put something off it’s like it doesn’t exist to me any more so never gets done.
get a routine in place, get a family calendar/notice board and set up a chores rota, even for the little ones. My 3 year old helps out with chores along with the older ones - you cannot and should not be expected to keep on top of the mess of 5 people without them helping.
meal plan and then do an online shop either for delivery or click and collect, yes this costs a little bit more but I’d rather sacrifice a snack or unnecessary food item than go shopping with 4 kids. This way you only have to do little top ups in the week so there’s usually always food in.
kids fighting - this one I can’t really help with, mine fight CONSTANTLY. I use time out, separate them and take away toys/playtime if it continues. Most of all I try to teach them to respect each other (easier said than done) but I’ve come to the conclusion that 4 siblings in the house together will fight and argue, it’s part of having a big family!
showers - I shower every other day, sometimes every 3 days i’m not gonna lie. I wash my hair once a week. It is what it is - some dry shampoo and a good deodorant work wonders!
most importantly - breathe OP. It’s hard, and that’s okay. You’re doing your best and by the simple fact that you’re worrying you’re not doing enough, shows that you ARE enough and you ARE a good mom. You’re not alone