Let G be a graph. A zero-sum flow of G is an assignment of nonzero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A zero-sum k-flow is a flow with values from the set
$$\{\pm 1, \ldots , \pm (k - 1)\}$$
. In this paper, we prove that every 5-regular graph admits a zero-sum 6-flow.
