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