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, \( \cos{x}=\sin{y}=\boxed{\frac{5}{13}} \).