score:3
In marketing, this is referred to as the number of "touches" required to make a sale or convince someone. It is not unique to religion, nor does it guarantee success. In marketing, this is called "funneling":
In fact, this approach only works on a small subset (typically a one-digit percentage) of the number of contacts.
The number of touches documented in market research is usually 6 to 8, which corresponds to "more than five meaningful contacts" in the question posted.