http://www.jerrydallal.com/LHSP/p05.htm

Maybe I can summarize it like this. First of all, Fisher started using 0.05 when deciding statistically meaningful. p=0.05 is 2 * standard deviation and 1 over 20. Thus it looks good enough. Also, once it’s accepted, it was not welcomed to using p=0.06 or p=0.07. In addition, using p=0.05 is easy for scientific discoveries as, say, p=0.01 needs really good data to support the alternative hypothesis.