Let

*x* = length of the army column in km

Going from front to rear:

relative velocity = 10 + 5 = 15 kph

relative distance traveled = *x* km

Going from rear to front:

relative velocity = 10 - 5 = 5 kph

relative distance traveled = *x* km

Note: time = distance / velocity

$t_\text{front to rear} + t_\text{rear to front} = 10 ~ \text{minutes}$

$\dfrac{x}{15} + \dfrac{x}{5} = \dfrac{10}{60}$

$\dfrac{4}{15}x = \dfrac{1}{6}$

$x = 0.625 ~ \text{km}$

$x = 625 ~ \text{m}$ ← *answer*