This may be a duplicate question but this seems like a time-sensitive matter (and the OP has tried some suggestions at the link) so I'll give this a shot.
My son was 4 and we intended to put him into preschool, but he would not poop on the toilet, whereas peeing was fine. He was afraid that it would hurt because a person I shall not name would put him on the toilet when he was younger and having constipation, which is something one should never do, so he associated the toilet with agony.Then I decided to show him some toilet training videos for kids on youtube and a few were nice, then one starts off well and then the person explodes, what a funny joke to play on a parent and child - ha. ha. ha. (I was an idiot for going to youtube for this, obviously). So he was even more afraid! I will accept my parent of the year award now, please.
What I finally did, after trying much other positive reinforcement, worked in just a day or two. This may not be an option around two older boys and a 3yo girl, but you may be able to work it out if some kids go off to summer camp, etc.
As a parent with only one child, we were fine with him not wearing anything other than a shirt for this short period of time while inside the privacy of our house. I think ethically this was fine since he was used to either of us changing him all the time and clearly didn't care.
I made sure he had nothing to go in, no pullup or underwear, nothing. He either had to choose the toilet or the floor.
He held it in a while (you should take steps to make sure his stool will be soft during this process, I can't remember what I did exactly it being 5 years ago), and then went and found a diaper that had fallen behind the changing table in his room and put it on and went. So I made sure there were no more diapers hidden anywhere (you'll need to hide all pullups and underwear, pants, etc).
So he held it in a while again, and then finally was pacing around and had to make a choice between the floor and the toilet. He finally ran to the toilet and the situation never came up again.
I told my sister this, and her current 4yo boy chose the floor (he had gone and hid in another room). So... that is the risk you take if you decide to try this. Remember, though, he may hold it in a while so you will want to make sure that his stool will be soft or you may just end up making the situation worse.
I always feel paranoid giving my first answer on a site so if something in here is terrible parenting advice I'll be happy to delete the whole thing.