I feel your pain, I had all 5 of mine in 6 years; they're now 24, 23, 21, 19 and 18.
You have a lot of great advice here. I worked outside my home, too, so depended on a great preschool as soon as they were old enough. I worked nights, stayed home with whoever was the baby during the day, so preschool gave me time to spend with the littlest ones, and they loved having their own class and projects to tell me about, and weren't on each other's nerves all day.
If there was bickering about a toy, it went into a box on top of the fridge for a day or two, they learned fast that I meant no fighting over toys. They did thump on each other now and then but they joke that the first full sentences they learned were,"that's rude, crude, and socially unacceptable," and "go to your room and come back when you can be a decent human being."(sometimes that meant I picked whoever up and plopped them on their bed if they were reluctant to leave the battle).
The house was noisy, is still when they're all together. Oh, well, lots of kids.
The housework was dead last on the list except for laundry and dishes.
I did group projects, like summer campish stuff, painting their own tee-shirts (which all said Wandering Wildcats on the back) and then going on field trips--God bless the ladies at Kenmore in Fredericksburg who let them try on costumes and fed us gingerbread, at that point they were 6,5,3,2 and 10mos. I must have been nuts.
The baby spent a lot of time hanging in a bouncy swing in doorways, in on the action but out from underfoot.
I'd leave the pack with my ex, and take whoever needed it most grocery shopping with me for some one on one that included lunch at McD's(I found if one of them was being naughtier that usual then it was time for special attention, and it seemed to work as a great attitude adjustment). I love Paula's idea of a special prayer/goodnight time.
I read them to sleep before I left for work, baby on my lap with a bottle, everyone else tucked in bed. I'd sit in the hallway because they were in two rooms, but I could see everyone and they could see me. As they got older, the little ones went down first, and that gave me time with the older ones, catching up on school and making sure things were okay.
My kids today are very proud that they were pretty independent very young--making their own lunches, they all did their own laundry at 10, everyone knows how to clean a bathroom and do dishes--even little ones can stand on a chair and wash the plastic things, splashing in bubbly water a bonus!
When the 6 year old comes home, have a group snack time. Gives everyone a break and him a chance to wind down. The 4 and 2 year old can help put snack together and set the table.
You're doing a good job, it's hard but you'll make it. My favorite escape was/is reading, a library is a great place to get some quiet, they have lots of programs and storytimes, check it out.