To solve this problem, we use the Pythagorean theorem for right-angled triangles, which states that the square of the hypotenuse equals the sum of the squares of the two right sides.

Step-by-Step Calculation:

Let the hypotenuse be (c = 5), one right side (a = 3), and the unknown right side (b).

According to the theorem:
[c^2 = a^2 + b^2]

Substitute the known values:
[5^2 = 3^2 + b^2]
[25 = 9 + b^2]

Solve for (b^2):
[b^2 = 25 - 9 = 16]

Take the positive square root (since length is non-negative):
[b = 4]

Answer: 4.

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