The development of the Saturn V rocket in reality took much longer than 10 years if you factor in previous research. Many of the principles that made that rocket fly were hashed out by Nazi German engineers working on the V2 rocket, specifically concepts developed by Werner Von Braun. After the war, he was integrated into what would eventually become NASA, and after helping develop the Jupiter line of rockets which the Saturn line was based on, ended up being appointed as the project chief behind the Saturn V.

It's quite morbid that the technology that put man on the moon was originally intended to destroy life (developed by a particularly odious political regime no less), but that's how it turned out.