Your current situation is all about stress, resentment and point-scoring. This must change for all your sakes.
What are the comparable hours? If he does twelve hours a day with a horrendous commute and you walk to work for eight hour days then yes, it is fair that you do more in the home. That's a mindset change … for you. Can you do that?
If you both do comparable hours though, then things need to be fairer - and that's a problem. Because you have five children, including a stropping adolescent. 'I'll just not do anything then, so there, nyer.'
You can't change his personality, his upbringing plus the fact you've had four children with him under this way of life. It's all embedded now.
So what else CAN you change?
Don't do the childish 'well I just won't do anything my week, then'. That's a toxic lesson for your kids. Be better.
You need help. And it ain't coming from him. You're both in full time work, and you're probably both knackered.
You need a different strategy:
Outsource that need for help to people who like doing things like cleaning, washing & ironing, gardening, shopping, cooking, are good at it and can do it faster and better than either of you can. They're out there. You need staff.
Yes, it's a cost - but balance that against the fact that you're both earning and the improvement in your relationship, the home and family life will be huge, because you'll have time for each other without a big lump of domestic resentment getting in the way.