jmc

Let $x$ be the common difference. Then $a=c-2x$, $b=c-x$, $d=c+x$, and $e=c+2x$, so $$a+b+c+d+e=(c-2x)+(c-x)+c+(c+x)+(c+2x)=5c.$$But this sum is also 30, so $5c=30$, which means $c=6$. Therefore, the answer is $\boxed{\text{(C)}}$.

To see that the values of the other terms cannot be found, note that the sequences 4, 5, 6, 7, 8 and 10,8,6,4,2 both satisfy the given conditions.