Is the answer 5?

Geometry Level 4

In $\Delta ABC$ , $AD , BE , CF$ are concurrent such that $D,E,F$ are points on $BC,AC,AB$ respectively.

If $CE=1$ , $CD=2$ , $BD=3$ , $AF=4$ , $AE=6$ ,then what is the length of $BF$ ?

Note: Figure not to scale.