How many weeks the field becomes bare?

Let s be the amount of grass one sheep eats in one week. Let O be the original amount of grass and g be the growth rate of the grass per week.

$240s \times 5 = O + 5g =====> 1200s = O + 5g \dots \dots [1]$

$200s \times 7 = O + 7g =====> 1400s = O + 7g \dots \dots [2]$

$[2] - [1]$

$=====> 200s = 2g =====> 100s = g$

$=====> O = 700s$

Now let w be the number of weeks

$170sw = O + gw =====> 170sw = 700s + 100sw$

$=====> 70w = 700$

$w = 10$

Therefore our answer is $\boxed{10}$ weeks.