I wouldn't go so far as tutor @ikleyn to say that the problem has no relation to math.
However, as she points out, ANY next two numbers make a valid sequence. So you can get some good mental arithmetic exercise looking for a pattern or rule that produces the given sequence.
However, trying to determine the "right" answer is only a matter of guessing -- and that is not mathematics.
Spend no more than a minute or two looking for a pattern that can produce the given sequence of numbers, then continue that pattern to find the next two numbers.
Realize, however, that any pattern you find might not be the right one....
With this particular example, there is a simple pattern that is VERY PROBABLY the "right" answer. Look at how each number compares to the number before it....
4 is 3 more than 1
2 is 2 less than 4
5 is 3 more than 2
3 is 2 less than 5
...
The odd-numbered terms go 1,2,3,4,...
The even numbered terms go 4,5,6,...
So the next term, which is the 8th, an even-numbered term, is 8.
The next term after that, which is the 9th, an odd-numbered term, is 5.
Edwin