Answer
E
Work Step by Step
$x=5\sec 38^{\circ}\implies \sec38^{\circ}=\frac{x}{5}$
But $\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent side}}$
This implies that $5$ is the length of the adjacent side to the $38^{\circ}$ angle and the length of the hypotenuse is $x$. This is the case in triangle E.
