Example 8 As shown in Figure 2.10.8, in $\triangle A B C$, $B C=5, A C=$ $12, A B=13$, points $D, E$ are taken on sides $A B, A C$ respectively, such that line segment $D E$ divides $\triangle A B C$ into two parts of equal area. Try to find the minimum length of such a line segment $D E$.