Answer
Scalar triple product is zero, thus, the vectors are coplanar.
Work Step by Step
$u= \lt 1,5, -2 \gt$, $v= \lt 3,-1,0 \gt$, $w= \lt 5,9,-4 \gt$
$(u \times v). w=( \lt 1,5, -2 \gt \times \lt 3,-1,0 \gt) \cdot \lt 5,9,-4 \gt$
$=1(4-0)-5(-12-0)+(-2)(27+5)$
$=4+60-64$
$0$
Hence, Scalar triple product is zero, thus, the vectors are coplanar.