What is the smallest possible positive integer x>5 , that leaves a remainder of 5 whenever it is divided by 14 , 8 or 77 ?

Answer 1

14 = 2x7
8 = 2x2x2
77 = 7x11

LCM = 7x11x8 = 616

adding 5+616 = 621

check:
621÷8 leaves remainder of 5
621÷14 leaves remainder of 5
621÷77 leaves remainder of 5

the number is 621