AD is the median of triangle ABC drawn to BC, so D is the midpoint of BC. A line through B parallel to AD meets CA produced at E. If CA = 5 cm, what is AE?

Work in triangle $CBE$, where A lies on $CE$ and $D$ lies on $CB$, and $AD$ is parallel to the side BE. BPT gives $\frac{CA}{AE}=\frac{CD}{DB}$. Since $D$ is the midpoint of $BC,CD=DB$, so the ratio is 1 and $AE=CA=5$ cm. The values 2.5 and 10 come from halving or doubling as if a midpoint theorem applied to $AE$; the length of $BC$ never enters the proportion, so the last option is wrong.