  Very accurate transition frequencies of HC$_5$N were determined between 5.3
and 21.4 GHz with a Fourier transform microwave spectrometer. The molecules
were generated by passing a mixture of HC$_3$N and C$_2$H$_2$ highly diluted in
neon through a discharge valve followed by supersonic expansion into the
Fabry-Perot cavity of the spectrometer. The accuracies of the data permitted us
to improve the experimental $^{14}$N nuclear quadrupole coupling parameter
considerably and the first experimental determination of the $^{14}$N nuclear
spin-rotation parameter. The transition frequencies are also well suited to
determine in astronomical observations the local speed of rest velocities in
molecular clouds with high fidelity. The same setup was used to study HC$_7$N,
albeit with modest improvement of the experimental $^{14}$N nuclear quadrupole
coupling parameter. Quantum chemical calculations were carried out to determine
$^{14}$N nuclear quadrupole and spin-rotation coupling parameters of HC$_5$N,
HC$_7$N, and related molecules. These calculations included evaluation of
vibrational and relativistic corrections to the non-relativistic equilibrium
quadrupole coupling parameters; their considerations improved the agreement
between calculated and experimental values substantially.
