It isn't but it kind of is. It is a 95% chance that you should reject the null hypothesis. For example if we flip a coin a 5 times and get heads every time that gives you a p value .03 for rejecting the null hypothesis that the coin is fair. If I run the five coin flip experiment a 100 times and never once reproduce a significant result is it because gee science is hard, or is it because you hit one of those 3% of cases. The same goes for real science if you can't reproduce it more often than not then you might be close but you haven't figured it out yet.
Ok, so we can agree that if you got positive a result with p<0.05 and you repeat the experiment 100 times you expect to reproduce a positive result (i.e. getting a new p-value below 0.05)
a) if the null hypothesis is true, 5 times
b) if the null hypothesis is not true, anywhere between 0
and 100 times (depending on what is the true alternative)
This is quite different from your previous assertion that the expected number of successful replications would be 95 out of 100.