An n ×n entrywise nonnegative matrix A is called doubly nonnegativeif A is also semidefinite positive as well. A graph G is called structural cp if all ofits doubly nonnegative structural matrices are completely positive, where a struc-tural matrix A= (aij) of G is defined as aij=1, if (i,j) ∈E(G) and 0, if (i,j) E(G) for all i≠j. This paper fully characterizes the structural cp matrices of order5.