Is there anyway to show my ex I've gotten better

We broke up 3 weeks ago after almost 5 years together. We are both pretty young and I am a very antisocial person and that hurt the relationship a lot. These past few months I've been depressed and convinced myself I was faking it so I never brought it up and that led to me being a bad partner when I wasn't the best already because of some problems I was struggling to fix already. We've talked up until today because we still loved each other, but a few days ago the messages dried up and they've decided we shouldn't get back together fully. They've said they're much happier without me and feel more motivation and that hurts as much as I am happy for them, because I wanted to be that pillar of support but I couldn't. I messaged them desperately to come back, sent long emails and letters and messages but I think that put them off me more.

I've finally realised my mistakes too late and I know I can fix them and I need to work on myself, but how could I show them I have? We've finally gone no contact today so should I wait until they break it? or should I break it when I've grown as a person.

Sorry if this post is a little confusing, it's my first time trying something like this and if you need anymore info just ask.