Erm, no. P=0.05 is borderline meaningless, there could as much as 30% chance you are wrong about the actual difference being there depending on the true probability of the initial hypothesis.
P-values should be used with strong caution.
FiveThirtyEight (and Scientific American, and others) did some pretty interesting articles about this recently if you haven't seen it:
http://fivethirtyeight.com/features/science-isnt-broken/
Just from personal experience, the use of p-values is really broken in biology/chemistry. The things I've heard principal investigators say...
Everything is just so much more sensible if you allow yourself to assign probabilities to hypotheses, rather than assuming a hypothesis from the outset and computing opaque statistics relating to your data.
I'm having trouble parsing this, are you talking about the power of the test?
This is a common problem in many fields, and you can use false discovery rate control methods to account for it: http://www.statisticsdonewrong.com/p-value.html