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