5. The area of a triangle is uniquely determined by the lengths of its three sides. Is the volume of a tetrahedron uniquely determined by the areas of its four faces?
(Construct a tetrahedron $ABCD$ such that $AB=CD$, $AC=AD=BD=CB$. Take the midpoint $E$ of $CD$, and the midpoint $G$ of $AB$, let $BE=a$, $\angle EBC=\theta$, then $EG=a \sqrt{1-\tan ^{2} \theta}$, $CD=AB=2 \tan \theta$. Therefore, $V=\frac{1}{3} S_{\triangle ABE} \cdot CD=\frac{2}{3} \cdot \sqrt{S^{3} \tan \theta\left(1-\tan ^{2} \theta\right)}$, where $S=a^{2} \tan \theta$ is the area of one of the four faces of the tetrahedron. Thus, $V$ depends on $\theta$. Hence, the volume of the tetrahedron cannot be uniquely determined by the areas of its four faces.)