Are you sure? Wouldn't the shiny charm increase the odds for each individual Pokemon?
5(1/4096) + 5(2/4096) = 5(3/4096) = 15/4096 = 1/273 chance per battle
I hardly run into hordes, so I wouldn't really know, but this seems more logical to me. Unless you can list an actual source, there is nothing to say that your answer is correct.