it looks to me like the interval between each of the number is the sum of the terms up to that number.
term 1 is equal to 5.
term 2 is equal to 5 + (1) = 5 + 1 = 6
term 3 is equal to 6 + (1 + 2) = 6 + 3 = 9
term 4 is equal to 9 + (1 + 2 + 3) = 9 + 6 = 15
term 5 is equal to 15 + (1 + 2 + 3 + 4) = 15 + 10 = 25
term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40
each succeeding term is the sum of the value of the previous term plus the sum of the value of the term numbers from 1 to the term number of the previous term.
for example, the value of term number 3 is the sum of the value of the previous term, which is 6, plus the sum of the value of the term numbers from 1 to the term number of the previous term, which is 2.
add the term numbers from 1 to 2 and you get 3.
add 3 to 6 and you get the value of term number 3 which is 9.
it's convoluted, but the logic seems to work so i'll go with it.