$\displaystyle 5 cos (x + 3) = 1$
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$\displaystyle 5 \cos (x + 3) = 1$
$\displaystyle \cos(x + 3) = \frac{1}{5}$
$\displaystyle \arccos(\cos(x + 3)) = \arccos(\frac{1}{5})$
$\displaystyle x + 3 = \arccos(\frac{1}{5})$
$\displaystyle x = \arccos(\frac{1}{5}) - 3$
$\displaystyle x \approx -1.63$
Yeah ... there's something not right there, are you sure you checked the right solutions against the exercise ?