Explanation

(c)
Since, $- 1 \leq \cos{\theta \leq 1}$
$\Rightarrow \ - 5 \leq 5\cos\theta \leq 5$
$\Rightarrow \ - 5 + 12 \leq 5\cos{\theta + 12} < 5 + 12$
$\Rightarrow \ \ 7 \leq 5\cos{\theta + 12} < 17$
Hence, minimum value is 7.
Alternate
For minimum value of given expression, we take
$\cos{\theta = - 1}$