I had a feeling that you homeschooled, given how you mentioned that sending them to school still wouldn't get you out of the house for work because of your youngest. Others caught the "public" word, though.
I don't know how many school-aged kids you would have, but gosh I would think that school clothes, activities, possible book/lab/whatever fees, and the possible/probable (if my son going to the Y and seeing what the other kids have) increases in the "I wants" would all result in MORE money going out than you do now. I think that sending them to school-school would be on the very bottom of my list of things to do that would help out financially, especially since, as you said, it still wouldn't get you out of the house.
This is a great point. I initially thought OP homeschooled too, then read all the "take them out of private school" responses and thought I missed something until the OP cleared that up. We are also a family of 5, I homeschooled until this year when our situation changed and the girls all went to public school. We haven't had an increase in the "I wants" (thankfully) BUT - the spending overall has increased in small ways.
Like the OP I used to spend about $100-150 a week in groceries for a family of 5 - $200 if we needed TP & toiletries. I now average $200-250. Groceries have gone up a little bit and that does count for some of it, but the majority of it is that I'm packing lunches for everyone every day. It used to be that the girls and I would sit down and have lunch at home, but things that I may have made at home - especially if it's a hot lunch - don't travel as well, so just rethinking lunch has increased the grocery bill. (the school lunch would be more expensive and none of the girls would eat it. )
I've also had to replace 3 out of 3 backpacks already this year. Thankfully, I had a very sturdy laptop backpack already that my highschooler uses now, but the 3rd graders backpacks I wasn't so lucky with. They started the year with ones they had (and had been using for 3 years for co-op, library, sleepovers etc), and by Christmas needed new ones. Clothing is also a bit more frustrating. When you're homeschooling and the kids hit that mid winter not quite spring growth spurt and 3 out of 4 of their pants are suddenly way to short, it's not a big deal. Wash the pants that fit more often (even mid day) or hang out in your jammies. But when the kids have to be out and about EVERY day, you have to make sure that every pair of pants is washed or fits. The Goodwill and consignment shops are great in this aspect, but it's just easier homeschooling when it's okay to wait another month to bring out the shorts & not buy more mid season.
It's also a total pain in the rear now to schedule medical and dental appointments. My highschooler missed a solid week and a half for a broken leg & surgery, then follow up appointments. It took her almost a month to catch up in her AP & Honors classes - and that's with the teachers sending work home (which ended up "busy work" not actual work. ugh) If she were homeschooled, she would have missed the two days of the break and surgery, and not wasted her time on busy work. She gets out of school 2 hours before the younger two (and leaves 2 hours prior) which drastically reduces the open window for scheduling her orthodontist appointments since I have to be home to get the younger two on and off the bus. Appointments at the same time, now mean wasting more of my day checking 3 kids out of 2 schools and waiting for them to get to the office. If you're interested in staying part of your kids education, check into the volunteer rules at your school. Most now will not allow you to volunteer with a sibling in tow, and I don't know how common this is, but parents are not allowed to volunteer at our school unless they are part a paying active member of the PTA. (Which I think sucks)
OP- Since you still have a younger one at home, I would look very seriously at the ability to continue homeschooling, or the necessity of public school in the near future. This is the time of year that co-ops and state organizations start having their used curriculum sales - maybe you can find the items you want for less than retail. You can also sell items that you aren't going to need anymore. Do you have a co-op? is there anything you can teach at the co-op? That was a great way for me to make some extra money at the time. You said photography, sociology & writing- If you have a co-op available would you feel confident in teaching a class in any of those subjects? Do you have your evenings available to offer yourself as a tutor to highschoolers? (public/private/homeschooled)
With regards to the kids activities - instead of just assuming they will have to be dropped are there alternatives? Can the kids reduce the number of activities? For example if they are (hypothetically) in Scouts, soccer, swim lessons, & music lessons - just go down to two instead of drop everything.
It may still be the right financial choice and the right choice for your family at this time to put the kids in school. On the other hand, it may also end up less expensive in the long run to keep them home at least until you know for sure it's not an option.