you're looking for the least common multiple of the numbers 5 & 6
that is . . . you're looking for the first time that a multiple of the value coincides with a multiple of the second value
multiples of 5
5
10
15
20
25
30
35
40
. . .
multiples of 6
6
12
18
24
30
36
42
. . .
as you can see, the first common multiple of both 5 & 6 is 30, so the answer is on the 30th day