The hypotenuse is the side opposite the right angle (the $90^\circ$ angle).

For $\sin J$, find the side directly across from vertex $J$ in the figure.

In Desmos, enter the expressions 5/13 and 12/13 to see their decimal values.

Use the figure to decide whether the side opposite $\angle J$ is the leg labeled 5 or the leg labeled 12.

Select the answer choice that equals $\dfrac{\text{(opposite side length)}}{13}$, since 13 is the hypotenuse.

Because $\angle K$ is a right angle, the side opposite it, $\overline{JL}$, is the hypotenuse, so $JL=13$. For $\angle J$, the side across from $J$ is $\overline{KL}$, so $KL=5$.

So the correct choice is $\dfrac{5}{13}$.