  We present spectro-photometry spanning 1-5 $\mu$m of 51 Eridani b, a 2-10
M$_\text{Jup}$ planet discovered by the Gemini Planet Imager Exoplanet Survey.
In this study, we present new $K1$ (1.90-2.19 $\mu$m) and $K2$ (2.10-2.40
$\mu$m) spectra taken with the Gemini Planet Imager as well as an updated $L_P$
(3.76 $\mu$m) and new $M_S$ (4.67 $\mu$m) photometry from the NIRC2 Narrow
camera. The new data were combined with $J$ (1.13-1.35 $\mu$m) and $H$
(1.50-1.80 $\mu$m) spectra from the discovery epoch with the goal of better
characterizing the planet properties. 51 Eri b photometry is redder than field
brown dwarfs as well as known young T-dwarfs with similar spectral type
(between T4-T8) and we propose that 51 Eri b might be in the process of
undergoing the transition from L-type to T-type. We used two complementary
atmosphere model grids including either deep iron/silicate clouds or
sulfide/salt clouds in the photosphere, spanning a range of cloud properties,
including fully cloudy, cloud free and patchy/intermediate opacity clouds.
Model fits suggest that 51 Eri b has an effective temperature ranging between
605-737 K, a solar metallicity, a surface gravity of $\log$(g) = 3.5-4.0 dex,
and the atmosphere requires a patchy cloud atmosphere to model the SED. From
the model atmospheres, we infer a luminosity for the planet of -5.83 to -5.93
($\log L/L_{\odot}$), leaving 51 Eri b in the unique position as being one of
the only directly imaged planet consistent with having formed via cold-start
scenario. Comparisons of the planet SED against warm-start models indicates
that the planet luminosity is best reproduced by a planet formed via core
accretion with a core mass between 15 and 127 M$_{\oplus}$.
