5. Let $M$ be the centroid of $\triangle ABC$, and $AM=3, BM=4, CM=5$. Find the area of $\triangle ABC$.
(1991 Shanghai Junior High School Competition Question)
5. Given $A M=3, B M=4, C M=5$, we have $A M^{2}+B M^{2}=C M^{2}$, which indicates that the two medians $A D, B E$ are perpendicular. Thus, $S_{\triangle A B C}=\frac{3}{2} \cdot A M \cdot$ $B M=18$.