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This great article gives you a quick and dirty understanding of the rule of fifths as a way to avoid Isobaric Counterdiffusion when diving Helium.
Isobaric Counter Diffusion - Scuba Engineer
Basically, "limit your rise in N2 to one fifth of the drop in Helium as you ascend."
So in the article, going from 20/25 to EAN32 was a no-no with a long deco run, because when He dropped from 25% to zero, the safe max jump in N2 was 5% rather than 55% to 68% (13%).
But when does it become unnecessary? I gather that for short deco, going from (for example) 15/55 to EAN50 is both common and generally accepted as safe. Theoretically, it exceeds the rule: He - 50% to 0%, while N2 - 30% to 50%. But your intermediate stops are very short, and no deco gases are hypoxic.
But using the first example discussed in the article, going from 20/25 would then progress to 32/8, and was noted to be safe. But this violates the rule too! The smaller the drop in Helium, the smaller the allowed rise in N2. Here, one fifth of a 17% drop in He is 3.7%, while the rise in N2 was 5%.
So when does it become silly that a small drop in Helium "allows" an even smaller rise in N2?
How does one properly use the rule to determine intermediate deco mixes?
You are assuming this 1/5ths rule is actually based on good science instead of conjecture and arm waving. That article is: 1) seventeen years old and 2) has no accounting for depth of the switches or the actual gas loadings and 3) is not supported by empirical data or even common modern practices.
If you stay out of trimix filled bells, keep your ENDs <100ft, and don't do any deep air switches, it's basically a hypothetical problem that just doesnt manifest in the world of recreational diving.