160604

I think the rules could be:
1) He only likes numbers with 5 in them
2) He only likes odd numbers
3) He only likes numbers in the 5 times table
4) He only likes numbers that have a 5 in the units

To test the rule, I would ask him if he likes the number 53. If he put it in the "don't like" column, we would know it wasn't rul 1 or 2. If he put it in the like box, we would know it wasn't rule 3 or 4. My next number to ask would be 50. This way, I would find out if it was odd numbers or numbers with 5 in that he liked.