The existence and persistence of five-fold (quintuple) bonding in isomers of model RMMR molecules of quite different geometry are examined theoretically. The molecules studied are RMMR, with R = H, F, Cl, Br, CN, and CH3; M = Cr, Mo, and W. The potential energy surface of these molecules is quite complex, containing two, three, even four local minima. The structural preferences in these molecules are rationalized, and electronic factors responsible for these preferences are elucidated. The linear geometry is always a minimum, but almost never the global minimum; there is a definite preference in RMMR for either a trans-bent conformation or perturbations of the trans-bent isomer with at least one of the R groups in a bridging position about the MM bond. The potential energy surface of these RMMR molecules is relatively flat, the lowest energy conformation being that which for a given molecule attains the best compromise between maximization of the MM bonding and minimization of orbital interactions that are MR antibonding. A surprising low-symmetry C(s) structure is identified, which along with the trans-bent isomer is one of the two most popular choices for the global minimum. Regardless of what isomer of the RMMR molecule is preferred, the MM quintuple bond persists.