5 sigma is a rule of thumb and it still needs to be qualified. IIRC, while the Higgs discovery was officially announced when the signal reached 5 sigma, most scientists in the field were already comfortable talking about a discovery well before that threshold as there were very high expectations (a prior I guess?) that the Higgs had to be there.

On the other hand, almost nobody believed the FTL Neutrino incident was real even if the signal was stronger than 5 sigma. Extraordinary claims still require extraordinary evidence.

IANP and everything.