  Astronomical mid-IR spectra show two minor PAH features at 5.25 and 5.7
$\mu$m (1905 and 1754 cm$^{\rm - 1}$) that hitherto have been little studied,
but contain information about the astronomical PAH population that complements
that of the major emission bands. Here we report a study involving both
laboratory and theoretical analysis of the fundamentals of PAH spectroscopy
that produce features in this region and use these to analyze the astronomical
spectra. The ISO SWS spectra of fifteen objects showing these PAH features were
considered for this study, of which four have sufficient S/N between 5 and 6
$\mu$m to allow for an in-depth analysis. All four astronomical spectra show
similar peak positions and profiles. The 5.25 $\mu$m feature is peaked and
asymmetric, while the 5.7 $\mu$m feature is broader and flatter. Detailed
analysis of the laboratory spectra and quantum chemical calculations show that
the astronomical 5.25 and 5.7 $\mu$m bands are a blend of combination,
difference and overtone bands primarily involving CH stretching and CH in-plane
and CH out-of-plane bending fundamental vibrations. The experimental and
computational spectra show that, of all the hydrogen adjacency classes possible
on PAHs, solo and duo hydrogens consistently produce prominent bands at the
observed positions whereas quartet hydrogens do not. In all, this a study
supports the picture that astronomical PAHs are large with compact, regular
structures. From the coupling with primarily strong CH out-of-plane bending
modes one might surmise that the 5.25 and 5.7 $\mu$m bands track the neutral
PAH population. However, theory suggests the role of charge in these
astronomical bands might also be important.
