[tedsanders]

That is not the definition of a p-value. :(

A p-value of 5% means that, IF the null hypothesis is true (IF!), then there's a 5% chance of getting results as extreme as measured.

A p-value of 5% does not mean than you should expect a rate of 5% false positives & negatives.

[jdmichal]

Isn't your second paragraph just a definition of a false positive?

And, it looks like power is the error rate for false negatives:

https://en.m.wikipedia.org/wiki/Statistical_power

Too late to edit my original to fix this.