  Since the Fermi discovery of $\gamma$-rays from novae, one of the biggest
questions in the field has been how novae generate such high-energy emission.
Shocks must be a fundamental ingredient. Six months of radio observations of
the 2012 nova V5589 Sgr with the VLA and 15 weeks of X-ray observations with
Swift/XRT show that the radio emission consisted of: 1) a shock-powered,
non-thermal flare; and 2) weak thermal emission from $10^{-5}$ M$_\odot$ of
freely expanding, photoionized ejecta. Absorption features in the optical
spectrum and the peak optical brightness suggest that V5589 Sgr lies 4 kpc away
(3.2-4.6 kpc). The shock-powered flare dominated the radio light curve at low
frequencies before day 100. The spectral evolution of the radio flare, its high
radio brightness temperature, the presence of unusually hard ($kT_x > 33$ keV)
X-rays, and the ratio of radio to X-ray flux near radio maximum all support the
conclusions that the flare was shock-powered and non-thermal. Unlike most other
novae with strong shock-powered radio emission, V5589 Sgr is not embedded in
the wind of a red-giant companion. Based on the similar inclinations and
optical line profiles of V5589 Sgr and V959 Mon, we propose that shocks in
V5589 Sgr formed from collisions between a slow flow with an equatorial density
enhancement and a subsequent faster flow. We speculate that the relatively high
speed and low mass of the ejecta led to the unusual radio emission from V5589
Sgr, and perhaps also to the non-detection of $\gamma$-rays.
