Any number can be the next number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest solution, based on a polynomial of order 3, is
T(n) = (-19n^3 + 143n^2 - 331n + 246)/3 where n = 1, 2, 3, ...
and accordingly, the next number is 53.
15
The next number in the sequence 5-7-13-31 is 69.
The nest number in the sequence is 18. Note that the difference between each number and the next number in the sequence follows the simple sequence of 1,2,3,4. Obviously the next in the sequence of increases is 5, so 13+5=18.
If the last number is 1/3 (it should be), the next number is 5 and 1/3
There really is no way of telling, but my guess is 22.
20
11
11
11.
15
The next number in the sequence 5-7-13-31 is 69.
21
22
17?
15
The nest number in the sequence is 18. Note that the difference between each number and the next number in the sequence follows the simple sequence of 1,2,3,4. Obviously the next in the sequence of increases is 5, so 13+5=18.
The next number in the sequence is 27.