First, calculate the radius of the circle using point A and the center (-2, 5):

\(r^2 = (7 + 2)^2 + (12 - 5)^2 = 9^2 + 7^2 = 81 + 49 = 130\)

The equation of the circle is:

\((x + 2)^2 + (y - 5)^2 = 130\)

Substitute the line equation \(y = -2x + 26\) into the circle equation:

\((x + 2)^2 + (-2x + 26 - 5)^2 = 130\)

\((x + 2)^2 + (-2x + 21)^2 = 130\)

Expand and simplify:

\((x^2 + 4x + 4) + (4x^2 - 84x + 441) = 130\)

\(5x^2 - 80x + 445 = 130\)

\(5x^2 - 80x + 315 = 0\)

Factorize:

\(5(x - 9)(x - 7) = 0\)

Thus, \(x = 9\) or \(x = 7\).

For \(x = 9\), substitute back into the line equation:

\(y = -2(9) + 26 = -18 + 26 = 8\)

Therefore, the coordinates of B are \((9, 8)\).