Answer
${\bf{u}}$ and ${\bf{v}}$ are parallel.
Work Step by Step
${\bf{u}}$ and ${\bf{v}}$ are parallel if there exists some scalar $\lambda $ such that ${\bf{u}} = \lambda {\bf{v}}$. So,
$\left( {1, - 2,5} \right) = \lambda \left( { - 2,4, - 10} \right)$
$1 = - 2\lambda $, ${\ \ }$ $ - 2 = 4\lambda $, ${\ \ }$ $5 = - 10\lambda $.
From the first equation we obtain $\lambda = - \frac{1}{2}$. This value satisfies the second and the third equation. Therefore, ${\bf{u}}$ and ${\bf{v}}$ are parallel.