const byte BUTTON = 2;
const byte LED = 10;
const int BLINK_TIME = 500;
const int BLINK_CYCLE = 5;
const int NO_BLINK = -1;

int prevButton = LOW;
int blink = NO_BLINK; // Current blink counter, -1 = blink disabled
bool ledState = false;
unsigned long tmrBlink = 0;

void setup() {
  Serial.begin(9600);
  pinMode(BUTTON, INPUT);
  pinMode(LED, OUTPUT);
  Serial.println("START");
}

void loop() {
  // Check transition from LOW to HIGH (only if not blinking)
  if (blink == NO_BLINK && prevButton == LOW && digitalRead(BUTTON) == HIGH) {
    // Activate blink
    blink = 0; 
    tmrBlink = millis();
    // A bit of debounce, if no hardware...
    delay(60);
    prevButton = HIGH;
    Serial.println("BUTTON");
  }
  if (blink > -1 ) {
    if (millis() - tmrBlink > BLINK_TIME) {
      Serial.print("Timer! ");
      blinkLed();
      if (!ledState) {
        ++blink;
        tmrBlink = millis();
        // End?
        if (blink == BLINK_CYCLE) blink = NO_BLINK;
      }
    }
  }
}

void blinkLed() {
  ledState = !ledState;
  digitalWrite(LED, ledState);
  Serial.print("B");Serial.print(blink);Serial.print("(");
  Serial.print(ledState);Serial.print(") ");
  Serial.println();
}