Translate $(5,2)$ 10 units left and 6 units down

Step 1 ：Translate the point (5, 2) by subtracting 10 units from the x-coordinate and 6 units from the y-coordinate: \((5 - 10, 2 - 6)\)

Step 2 ：The translated point is \(\boxed{(-5, -4)}\)