Answer
$-8\leq x\lt -3$
Or, in interval notation: $[-8,\ -3)$
Work Step by Step
We solve:
$14\lt 5-3x\leq 29$
We subtract 5:
$14-5\lt -3x\leq 29-5$
$9\lt -3x\leq 24$
And divide by $-3$:
$-3\gt x\geq-8$
$-8\leq x\lt -3$
Or, in interval notation: $[-8,\ -3)$