$(a)\;30^{\circ} \leq \theta \leq 60^{\circ} \\ (b)\;45 ^{\circ} \leq \theta \leq 60^{\circ} \\ (c)\;60^{\circ} \leq \theta \leq 72^{\circ} \\ (d)\;60^{\circ} \leq \theta \leq 90^{\circ} $

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Since the number of images formed is 5

We have $\large\frac{360}{\theta}$$-1 \leq 5 \leq \large\frac{360}{\theta}$

$\large\frac{360}{\theta} $$-1 \leq 5$

$360 \leq 60$

$\theta \geq 60^{\circ}$

$5 \leq \large\frac{360}{\theta}$

$\theta \leq \large\frac{360}{5}$

$\theta \leq 72^{\circ}$

$\therefore 60^{\circ} \leq \theta \leq 72^{\circ}$

Hence c is the correct answer

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