In a 30-60-90 triangle, the relationship between the lengths of the sides is as follows:
- The side opposite the 30-degree angle (the shortest leg) is \( x \).
- The side opposite the 60-degree angle (the longer leg) is \( x\sqrt{3} \).
- The hypotenuse (the longest side) is \( 2x \).
Given that the longest leg opposite the 60-degree angle is labeled \( 5\sqrt{3} \), we can set this equal to \( x\sqrt{3} \):
\[ x\sqrt{3} = 5\sqrt{3} \]
To find \( x \), divide both sides by \( \sqrt{3} \):
\[ x = 5 \]
Now, we can find the length of the hypotenuse \( y \). As noted, the hypotenuse in a 30-60-90 triangle is given by \( y = 2x \):
\[ y = 2(5) = 10 \]
Thus, the value of \( y \) is:
\[ \boxed{10} \]