First we have to find the values in which each factor equals zero.
In the first factor is going to be 5
In the second factor is going to be 7
Then we divide the number line by three parts
First part: Numbers less than 5
Second part: Numbers between 5 and 7
Third part: Numbers greater than 7
We choose any number belonging to each interval
First part: zero (0) because is less than 5
Second part: 6 because is a number between 5 and 7
Third part: 8 because it is a number greater than 7
Then we replace the numbers in the factors and operate
First part: (0-5)*(0-7) = (-5)*(-7)= 35 ( positive)
second part: (6-5)*(6-7) = (1)*(-1)= -1 ( negative)
third part: (8-5)*(8-7) = (3)*(1)= 3 ( positive)
Since we are searching for numbers that replaced in the equation give us negative results the intervals for the inequality must be
[5,7] which is represented in option C