I'm not a mom of many (yet!) but I nanny, so on any given day there are 4 kids under 3 over here, two of those being infants (3 months old) who need lots of one on one care (feeding/changing/holding/ect) Sometimes I even have the bigger sister, (6) like today. While I know it's WORLDS apart from having 4-5 kids of my own, I've learned a lot caring for so many kids everyday.
Simplify. Toys, food, everything.
I have fewer toys now than when it was just dd. The kids really do play with each other more, and the toys I keep are more so that the parents think I have SOME toys.

Anything with a million pieces usually doesn't last long. Puzzles and games with little parts go on a high shelf. The kids are always allowed to have them, they just have to ask first. It helps me to know when they are out. We have 'bins' for toys in the same category: Instruments, dress up, tools, dolls, kitchen, ect. Arts and crafts are usually dont outside in the back yard on a plastic picnic table. I don't care if paint or glue spills, and clean up is easy with a hose. We generally do messy crafts (paint) first thing in the morning, and then all get hosed off and jump in the pool.
Regarding food. I have a few things that I make for breakfast and lunch and rotate them. So, for breakfast, I have 3 'menus' I plan, scrambled eggs and toast, oatmeal or cereal, and waffles. On Sundays, I make 3 chicken breasts, a pot of rice, a pot of steamed veggies, and a pot of noodles (we like the whole wheat spiral kind). That food lasts me for a week, and I don't have to scramble around trying to make something at the last minute with kids screaming at me. My 5 lunch menus are:
Monday: Chicken and rice with veggie
Tuesday: Pasta with tomato sauce
Wednesday: Picnic day chicken salad sandwiches and celery/carrots with dip
Thursday: Chicken, rice and veggies again
Friday: Chicken noodle soup, using the remainder of the veggies/noodles/chicken I have
Snacks are easy, either fruit or yogurt. Now that it is summer, I've started making smoothies too, out of fruit, yogurt, and a bit of juice.
As for the cleaning, sigh. I wish there was an easier way. We have all tile and hardwood, and 2 big dogs and a cat. The hair really accumulates quickly, so I vacuum and mop every day. I've just come to realize that it's what has to be done, and I stopped getting frustrated about the mundane tasks that have to be repeated every. single. day. I figure if I just accept the fact that every day, I have to at LEAST 1. Vacuum, 2. Mop, 3. Do dishes/clean kitchen, 4. Cook, and 5. Do a load of laundry, life is so much easier. I try to do it while the kids are playing with each other, that way their nap time is also a rest time for me. I value MY time, even if it's only 20 minutes. I need that to be recharged, and if I don't have that time, I can really feel myself getting less and less patient. HTH