Step 1

The equation of the two lines are

$y=(2-\sqrt 3)(x+5)$---------(1)

$ y = (2+\sqrt 3)(x-7)$-----------(2)

This can be written as

$y = (2-\sqrt 3)x+10-5\sqrt 3$

$y=(2+\sqrt 3)x-14-7\sqrt 3$

Hence $m_1=2-\sqrt 3$ and

$\qquad m_2=2+\sqrt 3$

Step 2

The angle between the two lines is

$ \therefore \tan \theta = \bigg| \large\frac{(2-\sqrt 3 )-(2+\sqrt 3)}{1+(2-\sqrt 3 )(2+\sqrt 3)} \bigg|$

$ = \bigg| \large\frac{-2}{1+(4-3)} \bigg|$

$ = \bigg| \large\frac{-2\sqrt3}{2} \bigg|$

$ \tan \theta = \sqrt 3$

$ \therefore \theta = 60^{\circ} $ or $120^{\circ}$

Hence the angle between the lines is $ \large\frac{\pi}{3}$