Interesting but does 5 times work for everything or just some specific problems? I would agree that constantly asking why is a good thing but I'm just not sure about this 5 thing
It's just a rule of thumb, like the "rule of 7" when it comes to cognitive load. The point is to continue past the surface issue until you find the real problem. Fixing a lower-level problem (like not having automated testing) has much more value than fixing a higher-level problem (like fixing regressions when they occur in your software).
I'd always heard it put as the "seven whys", but yes, it does work.
The number is probably irrelevant, but the idea is to keep pushing for the deeper meaning (or root cause, in this case). If you can keep your reasoning from being circular ("the sky is blue because it isn't any other color"), you either get the answer, or learn that you don't know enough to get the answer.