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The LDR and 4.7K resistor ("resistor") form a voltage divider. There is a 5V drop across both (battery voltage). In the presence of light, the resistance of the LDR decreases, which results in more voltage (i.e., a greater proportion of the 5V) across the resistor. That triggers the 555. If you want to increase the sensitivity to light, increase the resistance of the resistor. If you want to decrease sensitivity, decrease the resistor.
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