(a) The equation of a circle with center (h, k) and radius r is given by \((x - h)^2 + (y - k)^2 = r^2\). Here, the center is (5, 2) and the circle passes through (7, 5).

Calculate the radius: \(r^2 = (7 - 5)^2 + (5 - 2)^2 = 2^2 + 3^2 = 4 + 9 = 13\).

Thus, the equation of the circle is \((x - 5)^2 + (y - 2)^2 = 13\).

(b) Substitute \(y = 5x - 10\) into the circle's equation: \((x - 5)^2 + ((5x - 10) - 2)^2 = 13\).

Simplify: \((x - 5)^2 + (5x - 12)^2 = 13\).

Expand and simplify: \(26x^2 - 130x + 156 = 0\).

Factorize: \(26(x - 2)(x - 3) = 0\).

Solutions are \(x = 2\) and \(x = 3\).

Find corresponding y-values: \(y = 5(2) - 10 = 0\) and \(y = 5(3) - 10 = 5\).

Points of intersection are (2, 0) and (3, 5).

Length of chord AB: \(AB = \sqrt{(3 - 2)^2 + (5 - 0)^2} = \sqrt{1 + 25} = \sqrt{26}\).