jmc

Call the common difference between any two consecutive terms $x$. We can express the first four terms in terms of $x$ and the fifth term: The fourth term is $5-x$, the third is $5-2x$, etc. So, we have $(5-4x)+(5-3x)+(5-2x)+(5-x)=10$, which simplifies to $-10x=-10$, or $x=1$. So the sixth term is $5+1=\boxed{6}$.