#### Answer

$$x=2\pi -4.37 ,\:x=4.65$$

#### Work Step by Step

Solving the equation using inverse trigonometric functions, we find:
$$5\cos \left(x+3\right)=1,\:0\le \:x\le \:2\pi \\ \cos \left(x+3\right)=\frac{1}{5} \\ x=\arccos \left(\frac{1}{5}\right)+2\pi n-3,\:x=2\pi -\arccos \left(\frac{1}{5}\right)+2\pi n-3 \\ x=2\pi -4.37 ,\:x=4.65$$