5. Given the planar vector $(1,1)$, the planar vector $\left(\frac{1-\sqrt{3}}{2}, \frac{1+\sqrt{3}}{2}\right)$ is obtained by transforming the vector $(1,1)$ through $\qquad$ transformation, the answer is
A. a clockwise rotation of $60^{\circ}$
B. a clockwise rotation of $120^{\circ}$
C. a counterclockwise rotation of $60^{\circ}$
D. a counterclockwise rotation of $120^{\circ}$
Since $(1+\mathrm{i})(\cos \theta+\mathrm{i} \sin \theta)=(\cos \theta-\sin \theta)+\mathrm{i}(\cos \theta+\sin \theta)=\frac{1-\sqrt{3}}{2}+\frac{1+\sqrt{3}}{2} \mathrm{i} \Rightarrow \theta=60^{\circ}$, so the answer is $C$.