When a number is successively divided by 7, 8 remainders are 5, 4.
If steps of division are reversed, find the remainders.
Numbers which when divided by 7 leave a remainder of 5 are:
12, 19 , 26, 33, 40, 47, 54, 61, 68,.... add 7 each time
Numbers which when divided by 8 leave a remainder of 4 are:
12, 20, 28, 36, 44, ...
looks like I could stop with 12
now we reverse the steps
12 ÷ 5 leaves remainder of 2
12 ÷ 4 leaves a remainder of 0
You might want to google "The Chinese Remainder Theorem"