Points, Lines & Planes · Superchallenge problem

Five points $A$, $B$, $C$, $D$, $E$ lie on a line in that order. The ten distances between pairs of these points are $3$, $4$, $5$, $7$, $8$, $9$, $12$, $16$, $19$, and $k$ (listed without regard to which pair gives which). Find $k$.