The Pentagon Lattice as a Substructure Lattice of Models of Peano Arithmetic

If $M prec N$ are models of Peano Arithmetic and Lt$(N/M)$ is the pentagon lattice $N_5$, then $N$ is either a cofinal or an end extension of $M$. In contrast, there are $M prec N$ that are models of PA* (PA in a language with countably many new predicate symbols) such that Lt$(N/M) cong N_5$ and $N$ is neither a cofinal nor an end extension of $M$.