5. In $\triangle A B C$, if $\angle B=45^{\circ}, B C=1, \triangle A B C$'s area $S=2$, then the diameter of the circumcircle of $\triangle A B C$ is $\qquad$ .
5. $5 \sqrt{2}$ Hint: From $S=\frac{1}{2} a c \sin B$, we get $c=4 \sqrt{2}$, so $b^{2}=a^{2}+c^{2}-2 a c \cos B=25$, so $b=$ 5 , so $2 R=\frac{b}{\sin B}=5 \sqrt{2}$.