5. Given $\cos (\alpha+\beta) \cos (\alpha-\beta)=\frac{1}{3}, \cos ^{2} \alpha-\sin ^{2} \beta$ is equal to ( ).
A. $-\frac{2}{3}$
B. $-\frac{1}{3}$
C. $\frac{1}{3}$
D. $\frac{2}{3}$
5. C. $\cos (\alpha+\beta) \cos (\alpha-\beta)=\frac{1}{2}[\cos 2 \alpha+\cos 2 \beta]=\cos ^{2} \alpha-\sin ^{2} \beta=\frac{1}{3}$.