The formulation contains its own escape clause and says so out loud: everything relates to five, given a sufficiently indirect method of relating. A rule that cannot fail is not a rule about the world, and the Principia knows it. What it is instead is an experiment the reader performs on themselves. Take the law seriously for a week, count the fives, and the count will rise, because attention has been directed and the mind supplies the connections. The doctrine works by working, which is the demonstration.
Robert Anton Wilson, who was close to the Discordian circle, put the point explicitly in his own writing: the Law of Fives is never wrong once you start looking for fives, and the same is true of any other number, which is what makes it worth teaching. He and Robert Shea carried the material into the Illuminatus! trilogy in 1975, where it operates as a running device alongside the sibling superstition of the number twenty-three, and where conspiracy is treated as the ordinary output of a mind given too much data and a hypothesis.
That is the serious content of a joke doctrine. Apophenia, the perception of meaningful pattern in noise, is a real and well-studied tendency, and the Law of Fives is a religious teaching that inoculates against it by inducing it deliberately. Discordians describe their own tradition as a joke disguised as a religion or a religion disguised as a joke, and decline to say which, and the ambiguity is doing the same work as the law.