But you're not a young child with probable SEN are you? I was slapped a few times as a child and remember it clearly, I absolutely despised my mother for it and lost all respect. If you'd ever done a safe guarding course then you would be aware this is physical abuse. It's sad that it was normalised for you.
OP his soiling himself 3 times in a day isn't really usual at 5, I'd be wondering if he's compacted and is leaking around the sides or if he doesn't recognise the urge - does he soil himself at school? Surely they don't think it's fine? Or do they just assume you're too lazy to potty train? That's seems to be a popular assumption rather than assuming there's some sort of SEN.
How is his general behaviour at school? Does he like going to school? Does he cope well there? If so I'd say that clear routine and being kept constantly occupied may be really helpful for him. It's possible that his behaviour may be him trying to get your attention whether he has SEN or not.
So I would make every weekend the same as much as possible, have a schedule where all his time is taken up with him doing something or another, either with you or his dad. Take him out to the park or to play football, a run around in the woods to burn off some of his energy then play trains or dinosaurs or whatever with him, get him to help you both with things around the house - notice and praise good behaviour. Talk to him and keep in engaged and busy.
I would also talk to his teacher about your concerns even if he is not struggling so much at school - DS is autistic and wasn't picked up at school till age 10, so don't assume that teachers are brilliant spotters of SEN, they will often put things down to the age of the kids, bad behaviour, poor parenting etc But if you tell them about your concerns that he may have SEN at least it's on their radar. The teacher may have some strategies she finds work well for him or she may have noticed some things that could be changed to help his behaviour.
If he likes messy play or making a mess then maybe if you have a garden he could have an area with empty bottles and pots that he can fill up with water, grass, stones etc and you can make 'potions' together. More of a summer activity perhaps but he sounds like a child that may really enjoy playing in puddles, mud and having fun making a mess.
OP you've reached the very end of your tether, use this awful situation as a catalyst to start making changing and working out what you can do to improve things. Talk to people and get as much help and support as you can. Tell people you are struggling, talk to his school, talk to the doctor about his soiling and see if you can get on a parenting course. Things need to change OP and DS doesn't know how so you need to. Good luck!