If we take the sequence terms apart and write the odd-numbered terms (the first, third, fifth, etc) and the even-numbered terms (the second, fourth, sixth, etc) in own sequences we will get:
5 10 15
15 13 11
So, in the first sequence every term is obtained by adding five to the previous, and in the second sequence every term is obtained by subtracting 2 from the previous term. According to this logic, the next number in the series 5, 15, 10, 13, 15, 11, 20.