For what it’s worth, control chart sensitivity rules are selected based on economic considerations. So the decision to use five points is influenced by both statics and how affordable it is to investigate why the control chart alerted. Sensitivity rules can be adjusted, applied, or ignored based on the specific situation and the analysts tolerance for false positives/negatives.

While I generally agree, I'm being more generic.

A single data point doesn't establish any direction or trend at all.

With two data points you can establish a trend and make a prediction about the next data point. However, any two data points form a line, so any two results can be used to make a trend, however wrong it may be.

Only when more points are used can you confirm the trend and reduce the probability of being (un)lucky.

Two in a row is a coincidence, three in a row might be a rule