After 5 days, she has 2/3 left means that the family eats 1/3 of the rice in 5 days, or they will finish all the rice in 5/(1/3)=15 days.
After two more days, i.e. 7 days, there are 20 kg left for the remaining 8 days.
This means that there were 20 kg / (8/15) = 20*15/8 = 37.5 kg for the whole 15 days.
Answer: there were 37.5 kg of rice at first.