Classification of $(v,5)$-configurationsfor $v\leq11$

We study $(v,k)$-configurations with $k = 5$, which are combinatorial objects. We prove necessary and sufficient conditions for combinatorial equivalence of $(v,5)$-configurations constructed from digraphs with two input and two output arcs in each vertex. We develop an algorithms for construction of $(v,5)$-configurations and identification of combinatorially equivalent of $(v,5)$-configurations. We also give a description of all $(v,5)$-configurations for $v\leq10$ and evaluate the number of combinatorially nonequivalent $(11,5)$-configurations.