While loop not breaking

Try This One its Simple:

void alarm()
{
  int count = 0;
  while ( digitalRead(alarmStop) && (count++ <5))
  {
    //A
    digitalWrite(buzz, HIGH);
    delay(500);
    digitalWrite(buzz, LOW);
    delay(500);
  }
}

But, There is a logical problem with this Code. Lets say that your code is at point A (metioned in comment) and at same time button is pressed. Now This code above will, still buzz and then stop.

To avoid This try using interrupts. To use interrupts on Arduino I prefer This Library. Download Here. Extract this and inside you will find a folder Named PinChangeInt. Copy This whole folder to your Documents\Arduino\libraries folder. Now, restart Arduino IDE and copy paste this code:

#include <PinChangeInt.h>

int buzz = 3;

bool alarmStatus = false;
#define PIN3 4
void pin3func() {
  digitalWrite(buzz, LOW);
  alarmStatus = true;
}

void setup() {
  pinMode(PIN3, INPUT); digitalWrite(PIN3, HIGH);
  PCintPort::attachInterrupt(PIN3, &pin3func, CHANGE);
}

int count = 0;
void loop() {
  if (count < 5)
  {
    if (!alarmStatus)
    {
      digitalWrite(buzz, HIGH);
    }
    delay(500);
    digitalWrite(buzz, LOW);
    delay(500);
  }
}

Because, of unavailability of hardware, I haven't tested this code. But, I hope It will work.

The problem with your code is your using delay(). This is a function that should most of the time be avoided for one simple reason: when the Arduino is executing the delay() instruction, it does nothing but wait. This means, among other things, that it cannot be reactive to user input. As outlined by ARK in his answer, interrupts could be used to overcome this problem. But you actually do not need them: the standard way to avoid delays is to use instead the millis() function to control timings. This approach is well described in the Blink without delay Arduino tutorial.

Here is how you can apply this technique to your alarm() function: In a nutshell, you can think of delay() to be roughly equivalent to this:

void naiveDelay(uint32_t ms)
{
    uint32_t start = millis();
    while (millis() - start < ms) {
        // do nothing
    }
}

The problem here is the “do nothing” part. You do not want your program to do nothing, you want it to monitor the “alarm stop” button. So the simple solution to your problem is to replace delay() by the code above, and then change it so that it monitors the button instead of doing nothing. Then you get something like this:

void alarm()
{
    for (int count = 0; count < 5; count++) {

        // start the buzzer
        digitalWrite(buzz, HIGH);

        // first delay
        uint32_t start = millis();
        while (millis() - start < 500) {
            if (digitalRead(alarmStop) == HIGH) {
                digitalWrite(buzz, LOW);  // stop the buzzer
                return;
            }
        }

        // stop the buzzer
        digitalWrite(buzz, LOW);

        // second delay
        start = millis();
        while (millis() - start < 500) {
            if (digitalRead(alarmStop) == HIGH) {
                return;  // buzzer already off
            }
        }
    }
}