5σ is not a rule. It's just a measurement of the probability that the result you observe is an accident. It means that it's very unlikely that it was just pure luck.
By the way, σ measurements are also used in many engineering jobs, and quality systems measurements. The kind of industry "goal" is to get 6σ (let's say when you manufacture consumer goods in large quantities, like millions every month). But for some other industries, 9σ is the benchmark - and from what I know, air companies have quality systems up to 9σ to ensure the lowest risk of something wrong happening.
How can they possibly have up to 9 sigma? 6 sigma is a failure rate about 1 in 10 billion, whereas 9 sigma would be 1 in 10^19 or so! That's oddly similar to the number of grains of sand on the earth![1]
The math will happily pop out absurd numbers. Remember that all stats carry assumptions with them, such as "this is a Gaussian process from negative to positive infinity" and "everything is absolutely perfectly independent" and other things that break down if your push them hard enough. What that is telling you is just how hard you're pushing the math rather than the real odds. I'm not 1 in 10^19 sure of anything.
By the way, σ measurements are also used in many engineering jobs, and quality systems measurements. The kind of industry "goal" is to get 6σ (let's say when you manufacture consumer goods in large quantities, like millions every month). But for some other industries, 9σ is the benchmark - and from what I know, air companies have quality systems up to 9σ to ensure the lowest risk of something wrong happening.