const int ledPin = 8;
const int button1 = 5;
int ledState = LOW;

const unsigned long interval = 1000;
unsigned long myBlinkTimer;
int  NoOfBlinks = 0;

void setup() {
  Serial.begin(115200);
  Serial.println("Setup-Start");
  Serial.println("press button to start blinking");
  pinMode(ledPin, OUTPUT);
  pinMode(button1, INPUT_PULLUP);
}

void loop() {

  if (NoOfBlinks == 0) { // if no blinking is active variable "NoOfBlinks" contains value 0
    if (digitalRead(button1) == LOW) {
      Serial.println("Button pressed start blinking");
      myBlinkTimer = millis();
      NoOfBlinks = 1; // assign value 0 to indicate blinking shall start
    }
  }

  // check if blinking shall be active
  if (NoOfBlinks > 0 ) {
    // check if it is time to change LED-state
    if ( TimePeriodIsOver(myBlinkTimer, interval) ) {
      Serial.print("NoOfBlinks:");
      Serial.print(NoOfBlinks);

      // if the LED is off turn it on and vice-versa:
      if (ledState == LOW) {
        Serial.println(" LED off switching on");
        ledState = HIGH;
      }
      else {
        ledState = LOW;
        Serial.println(" LED on switching off");
        NoOfBlinks++; // if blink has finished by switching off increment by 1
      }
      digitalWrite(ledPin, ledState);
    }

    if (NoOfBlinks > 5) {
      Serial.print("NoOfBlinks:");
      Serial.print(NoOfBlinks);
      Serial.println(" => stop blinking");
      Serial.println("press button to start blinking new");
      digitalWrite(ledPin, LOW);
      NoOfBlinks = 0; // assign value 0 to stop the blinking
    }
  }
}

// easy to use helper-function for non-blocking timing
boolean TimePeriodIsOver (unsigned long &startOfPeriod, unsigned long TimePeriod) {
  unsigned long currentMillis  = millis();
  if ( currentMillis - startOfPeriod >= TimePeriod ) {
    // more time than TimePeriod has elapsed since last time if-condition was true
    startOfPeriod = currentMillis; // a new period starts right here so set new starttime
    return true;
  }
  else return false;            // actual TimePeriod is NOT yet over
}