Summary: Edge disjoint paths have a closed relationship with edge connectivity and are anticipated to garner increased attention in the study of the reliability and edge fault tolerance of a readily scalable interconnection network. Note that this interconnection network is always modeled as a connected graph \(G\). The minimum of some of modified edge-cuts of a connected graph \(G\), also known as the \(h\)-extra edge-connectivity of a graph \(G (\lambda_h (G))\), is defined as the maximum number of the edge disjoint paths connecting any two disjoint connected subgraphs with \(h\) vertices in the graph \(G\). From the perspective of edge-cut, the smallest cardinality of a collection of edges, whose removal divides the whole network into several connected subnetworks having at least \(h\) vertices, is the \(h\)-extra edge-connectivity of the underlying topological architecture of an interconnection network \(G\). This paper demonstrates that the \(h\)-extra edge-connectivity of the pentanary \(n\)-cube \((\lambda_h (K_5^n))\) appears a concentration behavior for around 50 percent of \(h\leq \lfloor 5^n /2\rfloor\) as \(n\) approaches infinity. Let \(e=1\) for \(n\) is even and \(e=0\) for \(n\) is odd. It mainly concentrates on the value \([4g(\lceil \frac{n}{2}\rceil -r)-g(g-1)]5^{\lfloor \frac{n}{2}\rfloor +r}\) for \(g5^{\lfloor \frac{n}{2}\rfloor +r}-\lfloor \frac{[(g-1)^2 +1]5^{2r+e}}{3}\rfloor \leq h\leq g5^{\lfloor \frac{n}{2}\rfloor +r}\), where \(r=1, 2,\dots, \lceil \frac{n}{2}\rceil -2\), \(g\in \{1,2,3,4\}\); \(r=\lceil \frac{n}{2}\rceil -1\), \(g\in \{1,2\}\). Furthermore, it is shown that the above upper bound and lower bound of \(h\) are sharp.