When the button is pressed, it activates the SR Latch, maintaining the circuit in an "on" state. The 555 timer, set up as an oscillator, begins emitting regular pulses. These pulses are sent to the 4017 Decade Counter, which advances one count with each pulse. Once the counter reaches the fifth pulse, it sends a signal back to the SR Latch, turning off the sequence, and resets itself to start the count over. This results in the LED blinking five times.