Solve the system of equations shown on the whiteboard.

From the first condition (5 years ago):

$$x - 5 = 9(y - 5)$$ $$x - 5 = 9y - 45$$ $$x - 9y = -45 + 5$$ $$x - 9y = -40 \quad (1)$$

From the second condition (10 years time):

$$x + 10 = 3(y + 10)$$ $$x + 10 = 3y + 30$$ $$x - 3y = 30 - 10$$ $$x - 3y = 20 \quad (2)$$

Subtract equation (2) from equation (1):

$$(x - 9y) - (x - 3y) = -40 - 20$$ $$x - 9y - x + 3y = -60$$ $$-6y = -60$$ $$y = \frac{-60}{-6}$$ $$y = 10$$

$$x - 3y = 20$$ $$x - 3(10) = 20$$ $$x - 30 = 20$$ $$x = 20 + 30$$ $$x = 50$$

$$x = \boxed{50}$$ $$y = \boxed{10}$$