Question about how sketch code is executed:

Just note the time when the pin goes low. Each time through loop() you can then check to see if the time since then has been more than 5 seconds and act accordingly.

void loop() {
    static unsigned long timeInterrupterWentLow = 0;
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    if (digitalRead(interrupterPin) == LOW) {
        if (timeInterrupterWentLow == 0)
            timeInterrupterWentLow = millis();
        if (millis() - timeInterrupterWentLow > 5UL*60UL*1000UL) {
           // Do Whatever You Need To Do When This Fault Occurs
        }
    } else {
        timeInterrupterWentLow = 0;
    }
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}