A.M. Assaf, A. Hartman, and N. Shalaby determined in [1] the packing numbers \(\sigma(v, 6, 5)\) for all integers \(v \geq 6\), leaving six open cases of \(v = 41, 47, 53, 59, 62,\) and \(71\). In this paper, we deal with these open cases and thus complete the packing problem.