5. In trapezoid $ABCD$, the diagonals intersect at $O$, with $OA>OC$ and $OB>OD$. Take point $E$ on $AO$ such that $AE=OC$, and take point $F$ on $BO$ such that $BF=OD$. Then the relationship between the area $S_{1}$ of $\triangle AFC$ and the area $S_{2}$ of $\triangle BED$ is ().
(A) $S_{1}>S_{2}$
(B) $S_{1}=S_{2}$
(C) $S_{1}<S_{2}$
(D) Cannot be determined
5. B.

From the given information, we have
$$
\begin{array}{l}
S_{\triangle A B D}=S_{\triangle A B C}, S_{\triangle A E D}=S_{\triangle O C D}, \\
S_{\triangle A E B}=S_{\triangle B O C}=S_{\triangle A O D}=S_{\triangle A B F}, \\
S_{\triangle O C D}=S_{\triangle B F C} .
\end{array}
$$
$$
\text { Therefore, } \quad \begin{aligned}
S_{1} & =S_{\triangle A B C}-S_{\triangle A B F}-S_{\triangle B F C} \\
& =S_{\triangle A B C}-S_{\triangle A O D}-S_{\triangle O C D} \\
& =S_{\triangle A B C}-S_{\triangle B O C}-S_{\triangle O C D} \\
& =S_{\triangle A B D}-S_{\triangle A E B}-S_{\triangle A E D}=S_{2} .
\end{aligned}
$$