The sun won't go supernova, but it will become a red giant in about 5,000,000,000 years, which will have roughly the same consequences for life on earth.
To be honest, I can't quite predict if humanity truly survives within the next decade or two/three or a century. Let alone millions of times more than that amount.
We humans are very likely to be our own worst enemy. I would wish for the world to exist till the 5_billion year date that you mention.