In a 30-60-90 triangle, the lengths of the sides are in the ratio \(1 : \sqrt{3} : 2\), corresponding to the angles \(30^\circ\), \(60^\circ\), and \(90^\circ\) respectively.
If the length of the shorter leg (opposite the \(30^\circ\) angle) is \(5\), then the length of the hypotenuse (which is twice the shorter leg) is calculated as follows:
\[ \text{Hypotenuse} = 2 \times \text{(shorter leg)} = 2 \times 5 = 10 \]
Thus, the length of the hypotenuse is \(10\).
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