The two acute angles of a right triangle have degree measures of $x$ and $y$. If $\cos{x}=\dfrac{5}{13}$, what is the value of $\sin{y}$?

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Start by drawing a right triangle where $\cos{x}=\dfrac{5}{13}$.

The other acute angle must be the only angle that isn't labeled. $\sin{y}=\boxed{\dfrac{5}{13}}$

Because $x \text{ and } y$ must add up to $90\degree$, $x=90-y$ or $y=90-x$.

Use the known identity $\cos{(90-\theta)}=\sin{\theta }$. This formula translates to: the sine of one angle is equal to the cosine of its complementary angle (and vice-versa).

Therefore, $\cos{x}=\sin{y}=\boxed{\frac{5}{13}}$.