Anytime a complex machine is produced for a long time, there exists a problem where some of the parts no longer are manufactured after a period of time. This can happen for a variety of reasons, and is most common with electronics. For instance, buying a VME chassis today is difficult, and much more expensive than standard computer electronics today. Standards change over time to ones that are better, cheaper, faster, etc. The old goods become increasingly difficult to maintain.
I've worked in the aerospace industry for some time. Sometimes certain key parts suddenly are no longer available. There is a couple of different ways of addressing these issues, but they basically come down to some kind of a re-design. The objects that I have seen were more mass produced than the Saturn 5, and were about 15 years old, and some of them were no longer available.
Re-building the Saturn 5 would require tremendous work, almost as much as building a new similar rocket would be today. Modern techniques could make it lighter, stronger, more reliable, and cheaper than simply rebuilding the existing design would be. The Apollo spacecraft would be even more difficult, as it relied heavily on very dated technology.
The bottom line is, a re-design of the electronics is required to make it work, it'd be a vast improvement. The general physics, however, remain the same, and so there are some principals from the existing designs which are still applicable today. Saturn 5 lead to the Space Shuttle, and it is leading to SLS. And those technologies are inspiring the rockets we have today.