> Again, look, Ma, no standard deviations or Gaussian assumptions.

You're once again overlooking the context. In a physics context, 5σ has an oft-quoted numerical value that is acquired this way:

http://i.imgur.com/pcjr6cN.gif

Good luck acquiring the universally accepted numerical value without applying a Gaussian distribution as shown.

Remember that this thread began with someone nontechnical asking what the significance of 5σ was to the evaluation of a physics experiment, for which I provided an uncontroversial explanation in that context.