  Let $G$ be a graph. A zero-sum flow in $G$ is an assignment of nonzero real
number to the edges such that the sum of the values of all edges incident with
each vertex is zero. Let $k$ be naturel number. A zero-sum $k$-flow is a flow
with value from the set $\{\pm 1, \pm 2,..., \pm(k-1)\}$. It has been
conjectured that every $r$-regular graph, $r\geq 3$, admits a zero-sum 5-flow.
In this paper we give an affirmative answer to this conjecture, exept for r=5.
