I'd tackle it several ways.
Be kind to yourself because you've been through a lot. So if you don't feel upto doing much, that's fine. When you feel upto it, do more.
If you've got feelings of persistent sadness and you can't change the situation that causes it, antidepressants can help you cope with it. Unless you're willing to just put up with it, which is also an option.
Do the usual self care things. Sleep cycle, diet, exercise, showering, housework etc.
Try to change your mindset. Your son's made a decision that hurt you but that wasn't their intention rather a side effect, they made that decision believing it to be in their best interests. They must have missed you to be devastated by the breakup, otherwise they surely wouldn't have cared or might even have been happy. So they made a decision that they believed was right for them, even though on some level it would have hurt them. That shows strong character in them. Hopefully they're the sort of people to make a good life for themselves then and to overcome any adversity. Have faith in them that they are and will be ok.
If you still have an address for them I'd write to them one last time explaining that they're adults now and you respect their decision not to see you so you'll stop trying to contact them, but that your door is always open if they want to discuss anything or form a new relationship with you in the future. Wish them happiness and good luck for their futures. Then stop contacting them and focus on moving on. When they're older, they may return for answers or may see your situation for what it was, with greater life experience and so gain understanding that it was necessary for you to leave. Leave the possibility open but don't wait for it because it may never happen.
You need a hobby for the weekend. You're wallowing and it's not doing you any good. It's been 5yrs and your DC aren't dead. You did what was necessary by leaving your ex. Your DC aren't your life and were always destined to grow up and move away from focusing on their parents. In a practical sense, the situation you're in now isn't so different to people whose DC only visit once a year. It wouldn't be healthy for them to spend the other 364 days moaning and feeling sad and it's not healthy for you to either.
The sadness will never completely leave I don't suppose, but you can learn to live with it, as you've said, you have to. It doesn't need to define you or be the sole focus of your life though.