Given the curve \(y = x^{2} - 6x + 5\)

At minimum or maximum point, \(\frac{\mathrm d y}{\mathrm d x} = 0\)

\(\frac{\mathrm d y}{\mathrm d x} = 2x - 6\)

\(2x - 6 = 0 \implies x = 3\)

Since 3 > 0, it is a minimum point.

When x = 3, \(y = 3^{2} - 6(3) + 5 = -4\)

Hence, the turning point has coordinates (3, -4).