It was Fisher who suggested giving 0.05 its special status. Page 44 of the 13th edition of SMRW, describing the standard normal distribution, states
The value for which P=0.05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation ought to be considered significant or not. Deviations exceeding twice the standard deviation are thus formally regarded as significant. Using this criterion we should be led to follow up a false indication only once in 22 trials, even if the statistics were the only guide available. Small effects will still escape notice if the data are insufficiently numerous to bring them out, but no lowering of the standard of significance would meet this difficulty.
Now if you want to believe that Fisher and the rest of humanity was influenced by the fact that 1/20 is one of the total digits humans have, that's OK. (I doubt the fact that the decimal representation of 1/20th had anything to do with it but Dew probably disagrees ) Presumably that would leave you to conclude that our insect society might pick 1/6th or p = 0.1667 (base 10). But if the insects made the Fisher argument based on the normal distribution, it would appear to be independent of the number of digits.