Guiness World Record claims that Goldbach's conjecture is the oldest unsolved problem. A natural related question is what solved problem went unsolved for the longest time. In other words, of all the now-solved problems, which was open for the longest?
Perhaps it depends how we define the moment when a problem becomes "posed," but we could define this moment as the first time the problem is referenced in any record we have.
Some geometric construction problems - e.g. doubling the cube - were "posed" in antiquity but only solved in the $19$th century. This gets us a gap of about $\sim 2000$ years at least.
Re: the scare quotes above, there is a slight issue here about what exactly constitutes posing a problem. The texts I'm aware of all phrase it as a positive imperative, "figure out how to double the cube using only compass and straightedge." Since the punchline is that that can't be done, there's a disconnect between the way the problem was posed and the way it should have been posed. I personally think this still counts though.