I am not aware of that specific saying but there is certainly an approach similar to that in western air forces coming from the US Air Force but its about 10, not 5. I cannot find the source for that specific statistic right now, and I'll continue searching. In the meantime, if this reply does not measure up with the standards of the sub, I understand.

Multiple statistical studies of US air wars found that after reaching ten operational sorties, a pilots chances to survive a full tour in a combat zone grows drastically. This is not only true to air combat specifically, since far from majority pilots had five air-to-air encounters in their careers, much less ten (especially after the Korean War, since after that war aerial encounters became far less common for the AF). But rather to the whole combat environment.

How aware and familiar is the pilot with the threats, how internalized are the operational procedures, how confident he is and how well he employs his judgments are just a few of the personal factors that affect the chances of a pilot to survive.

The training in western air forces, especially the big exercises such as the famous Red Flag ,as proponed by Colonel Richard Suter, tries to replicate this environment. So that, among of other things, the pilot has relevant experience as close as possible to real operational one, so he will have better chances to survive and succeed in his mission as if he already had his ten operational sorties.