Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an obtuse triangle.

For the sides to form a triangle, the third side must satisfy 5 < x < 15. With x = 6, the longest side is 10, and 10² = 100 is greater than 5² + 6² = 61, so the triangle is obtuse. Thus, the correct choice is 6.

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