已知 $\sin \alpha=\frac{\sqrt{5}}{5}$, 则 $\sin ^{4} \alpha-\cos ^{4} \alpha$ 的值为( )
[解析] $\sin ^{4} \alpha-\cos ^{4} \alpha=-\left(\sin ^{2} \alpha+\cos ^{2} \alpha\right)\left(\cos ^{2} \alpha-\sin ^{2} \alpha\right)=-\cos 2 \alpha=2 \sin ^{2} \alpha-1=-\frac{3}{5}$.