The answer is 34.
The full sequence is called the Fibonachi series.
Your sequence is 3 5 8 13 21
3 + 5= 8
8 + 13 = 21
Therefore:
13 + 21 = 34
The next number will be 13+21 = 34
22
16.
17 cause it is the next prime number
37.
The next number will be 13+21 = 34
37
35
22
16.
17 cause it is the next prime number
37
37
18
37.
the next number is 21 because it is adding the last number stated.
13