I think you're probably harder on yourself than you need to be, saying that these other moms are all put together and you don't feel that you are. You have no idea what insanity they went through on the way to school, and those 5 kids might not be all theirs anyway (carpool?).
So, I'd decide what the bare minimum is for your own appearance in terms of makeup, and then add one thing. So if a ponytail and some blush is the minimum, add a quick swipe of lip gloss and call it a day.
What are your own kids responsible for? Are you trying to do everything in terms of planning and supervision? Or do they have age-appropriate assignments (and are you willing to let them feel the repercussions if they don't follow through)? For example, if a kid doesn't plan ahead to wear his lucky red shirt on Tuesday, then is he the kid who goes without it or are you the mom who throws in a load of wash at 6:45 a.m. because someone is whining? Kids learn faster if parents are happy to throw them in the car in their pajamas because they didn't get ready, you know? So if you back off from your need to be totally together and put some of this on the kids' shoulders, you'll do better after 2 weeks of them kvetching.
Set out clothes the night before - give the child 2 choices, and whatever is picked is what gets worn. No decisions. Put cereal or cut up fruit in a bowl the night before, covered. Let the kids feed themselves. Make a bunch of lunches ahead of time - my mother made 10 sandwiches on Sunday nights and froze them, wrapped. On each morning, 2 got pulled out and we 2 kids had defrosted lunch by 11 a.m. Buy snacks and fruit in large bags, then divvy up in small reusable plastic containers on Sundays (kids can help) and then put the single-serving containers where they can be grabbed and thrown into a lunch box. 1 sandwich/wrap, 1 snack, 1 fruit, done. Use reusable water bottles that can be filled at the tap - not bottled water and no juices. Cheaper, and easier for a kid to refill at the school water fountain.
Backpacks at the door, with shoes and coats, all set the night before. If you have an individual hook for each kid, great. If you have a little basket for hats/gloves for each kid, great. All their stuff goes in that the day before, long before there's any screen time. When they get home, they can each put their lunch boxes in the kitchen and empty them, putting containers in the sink to be washed, and they can refill their water bottles for the next day.
Have a file divider thing on the wall with a folder or large envelope for each kid that holds permission slips, school physical forms, notes for the teacher, anything else that has to go in.
Have a small basket in the downstairs bathroom (if you have a 2 story house) with the hair essentials (scrunchies, barrettes, brushes) and toothbrushes for a quick touch-up without someone going back upstairs.
Set the clock 5 minutes ahead and do not tell the kids that you've done that.
And the night before, when you decide to do one more thing before bed...don't. Go to bed, and get up 15 minutes before you usually do, just to get your head together.