  We present emission line ratios from a sample of 26 Lyman break galaxies from
$z\sim5.5-9.5$ with $-17.0<M_{1500}<-20.4$, measured from ultra-deep
JWST/NIRSpec MSA spectroscopy from JADES. We use 28 hour deep PRISM/CLEAR and 7
hour deep G395M/F290LP observations to measure, or place strong constraints on,
ratios of widely studied rest-frame optical emission lines including H$\alpha$,
H$\beta$, [OII] $\lambda\lambda$3726,3729, [NeIII] $\lambda$3869, [OIII]
$\lambda$4959, [OIII] $\lambda$5007, [OI] $\lambda$6300, [NII] $\lambda$6583,
and [SII] $\lambda\lambda$6716,6731 in individual $z>5.5$ spectra. We find that
the emission line ratios exhibited by these $z\sim5.5-9.5$ galaxies occupy
clearly distinct regions of line-ratio space compared to typical z~0-3
galaxies, instead being more consistent with extreme populations of
lower-redshift galaxies. This is best illustrated by the [OIII]/[OII] ratio,
tracing interstellar medium (ISM) ionisation, in which we observe more than
half of our sample to have [OIII]/[OII]>10. Our high signal-to-noise spectra
reveal more than an order of magnitude of scatter in line ratios such as
[OII]/H$\beta$ and [OIII]/[OII], indicating significant diversity in the ISM
conditions within the sample. We find no convincing detections of [NII] in our
sample, either in individual galaxies, or a stack of all G395M/F290LP spectra.
The emission line ratios observed in our sample are generally consistent with
galaxies with extremely high ionisation parameters (log $U\sim-1.5$), and a
range of metallicities spanning from $\sim0.1\times Z_\odot$ to higher than
$\sim0.3\times Z_\odot$, suggesting we are probing low-metallicity systems
undergoing periods of rapid star-formation, driving strong radiation fields.
These results highlight the value of deep observations in constraining the
properties of individual galaxies, and hence probing diversity within galaxy
population.
