Explanation

The sequence is formed by adding consecutive integers to the previous term:

3 + 2 = 5

5 + 3 = 8

8 + 5 = 13

13 + 8 = 21

21 + 13 = 34

This sequence is a well-known sequence called the "Fibonacci-like sequence" or "Recursive sequence". Each term is the sum of the two preceding terms, starting from 3 and 5.