Japanese set of cups mostly comes in 5, unlike Westerns that normally comes in 6 (half-a-dozen). The experts have some reasons for this: Japanese people believe to avoid even numbers in any occasion as it gives them bad luck. Especially when giving gifts to someone that is more respected, they are being very careful to not doing so.
Then why is it not 4? Apparently in Japan the number 4 symbolizes “death”, just as in America they skip number 13 (with reason that I don’t know of). Another idea is that the ideal Japanese family consists of 5 people; both parents, two sons and one daughter. Three is too little, and 7 is way too much.
Also because even numbers are divisible and in Japanese the word ‘divide’ is pronounced the same as the word to ‘break’, it doesn’t give them quite a good impression.