Can't get LED Sequence Program to run properly

I'm a newbie to Arduino so please bear with me! I'm trying to write a program where a push button controls 5 LEDs advancing from one to the other with each button press. When I run the program however, the 5 LEDs just start blinking sequentially on their own and the button has no affect whatsoever. My code is below... any clues?

const int buttonPin = 2; // the number of the pushbutton pin
const int ledPin1 = 3; // the number of the LED pin
const int ledPin2 = 4; // the number of the LED pin
const int ledPin3 = 5; // the number of the LED pin
const int ledPin4 = 6; // the number of the LED pin
const int ledPin5 = 7; // the number of the LED pin
// variables will change:
int buttonState = 0; // variable for reading the pushbutton status
int buttonPressCount = 0;
int numberOfLED = 5;
void setup() {
// initialize the LED pin as an output:
pinMode(ledPin1, OUTPUT);
pinMode(ledPin2, OUTPUT);
pinMode(ledPin3, OUTPUT);
pinMode(ledPin4, OUTPUT);
pinMode(ledPin5, OUTPUT);
// initialize the pushbutton pin as an input:
pinMode(buttonPin, INPUT);
}
void loop() {
// read the state of the pushbutton value:
buttonState = digitalRead(buttonPin);
// check if the pushbutton is pressed.
// if it is, the buttonState is HIGH:
if (buttonState == HIGH) {
if (buttonPressCount % numberOfLED == 0) {
// turn LED1 on:
digitalWrite(ledPin1, HIGH);
} else {
digitalWrite(ledPin1, LOW);
}
if (buttonPressCount % numberOfLED == 1) {
// turn LED1 on:
digitalWrite(ledPin2, HIGH);
} else {
digitalWrite(ledPin2, LOW);
}
if (buttonPressCount % numberOfLED == 2) {
// turn LED1 on:
digitalWrite(ledPin3, HIGH);
} else {
digitalWrite(ledPin3, LOW);
}
if (buttonPressCount % numberOfLED == 3) {
// turn LED1 on:
digitalWrite(ledPin4, HIGH);
} else {
digitalWrite(ledPin4, LOW);
}
if (buttonPressCount % numberOfLED == 4) {
// turn LED1 on:
digitalWrite(ledPin5, HIGH);
} else {
digitalWrite(ledPin5, LOW);
}
buttonPressCount++;
delay(400);
}
}

My code is below... any clues?

My biggest clue is the lack of code tags which suggests you didn't read the clearly-posted posting guidelines.

I'm guessing you've got a floating input pin.

How is the pushbutton wired ? Do you have a pull down resistor so that it is always in a known (not floating) state ?
A better way to do what you describe is to detect when the button becomes pressed rather than when it is pressed. See the StateChangeDetection example in the IDE.

When you have that working consider putting the LED pin numbers in an array so that you can cut the code by half if not more.

Once you have the push button wiring fixed up, look at the delay() calls you have in the code as this will cause the code to be very unresponsive to button presses.