In triangle $ABC$, $BD$ is a median.  $CF$ intersects $BD$ at $E$ so that $\overline{BE}=\overline{ED}$.  Point $F$ is on $AB$.  Then, if $\overline{BF}=5$, $\overline{BA}$ equals:
$ \textbf{(A)}\ 10 \qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ \text{none of these} $