01111. If we split the binary in groups of four, the third-to-last quartet is a continuation of the first pattern in the 1st and 2nd quartets. The last two digits perhaps are a continuation of the first two digits of the third quartet. But this is just a guess.... i'm probably wrong.
Ah. My first reaction was to put things in quartets (just like actual binary code) to discern patterns. So I ended up putting it in this form:
I noticed the continuation of the "1011" 3rd from the bottom as the repetition of the 1st "1011", so I just (erroneously) styled the last five digits as a continuation of the rest of that quartet and the first two of the next.
i figured it out so don't read this if you don't want to know the answer:
the answer is 11101. because he said it wasn't a simple repetition thing, i the next logical conclusion is that it's binary. because there were 5 question marks, i figured the last binary number was five digits long.
i figured the numbers would go in increasing order (they don't have to, but i guessed, and they did). so i looked at the previous 5 digits... in binary, that's 23. so i did the previous 5, etc: 19, 17... then the previous 5 digits would have made a larger number (29), so i figured i'd decrease it to four digits, which made 13 in binary. so by this point i have 19,17,13, and it's pretty clear that it's a pattern of prime numbers. sure enough, the list goes on: 11,7,5,3,2... so the next number in the pattern would be 29, or 11101.