He will eat 8 bananas on the first day, 14 on the second, then 20, 26 and 32 on the final days. These total 100 bananas all told and eaten in five days.
Method: Eating X on the first day, X+6 on the second, X+12 on third etc, up to X+24 on day 5. These total (5X+60) bananas. Solve the equation 5X + 60 = 100