I've had the same Gmail account now for 5+ years. I have a Google+ account associated with that Gmail account. I want to change my email address, so I created a new Gmail account. How do I associate it with my Google+ profile?
As you're creating a new GMail account anyway you can do this, but you have to do it from the Google+ end.
Click on the "Mail" link:
and you'll be redirected to this page where you can create a new GMail account which will be associated with your Google+ account:
It means you'll create another new GMail account, but as you're doing that anyway you can just abandon the first "new" account you created.