jmc

It is clear that the maximal positive difference is $6-1=5$. Moreover, we can use 6 to ensure that we can get all positive integer differences up to 5: $6-5=1$, $6-4=2$, $6-3=3$, $6-2=4$, $6-1=5$. So, there are $\boxed{5}$ possible differences.