jats:titleAbstract</jats:title> jats:pWe present rest-frame optical emission-line flux ratio measurements for five jats:italicz</jats:italic> > 5 galaxies observed by the James Webb Space Telescope Near-Infared Spectrograph (NIRSpec) in the SMACS 0723 Early Release Observations. We add several quality-control and post-processing steps to the NIRSpec pipeline reduction products in order to ensure reliable jats:italicrelative</jats:italic> flux calibration of emission lines that are closely separated in wavelength, despite the uncertain jats:italicabsolute</jats:italic> spectrophotometry of the current version of the reductions. Compared to jats:italicz</jats:italic> ∼ 3 galaxies in the literature, the jats:italicz</jats:italic> > 5 galaxies have similar [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>5008/Hjats:italicβ</jats:italic> ratios, similar [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>4364/Hjats:italicγ</jats:italic> ratios, and higher (∼0.5 dex) [Ne jats:scIII</jats:sc>]jats:italicλ</jats:italic>3870/[O jats:scII</jats:sc>]jats:italicλ</jats:italic>3728 ratios. We compare the observations to MAPPINGS V photoionization models and find that the measured [Ne jats:scIII</jats:sc>]jats:italicλ</jats:italic>3870/[O jats:scII</jats:sc>]jats:italicλ</jats:italic>3728, [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>4364/Hjats:italicγ</jats:italic>, and [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>5008/Hjats:italicβ</jats:italic> emission-line ratios are consistent with an interstellar medium (ISM) that has very high ionization (jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:milog</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:miQ</mml:mi> <mml:mo stretchy="false">)</mml:mo> mml:mo≃</mml:mo> mml:mn8</mml:mn> mml:mo−</mml:mo> mml:mn9</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjacba8aieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, units of cm sjats:sup−1</jats:sup>), low metallicity (jats:italicZ</jats:italic>/jats:italicZ</jats:italic> jats:sub⊙</jats:sub> ≲ 0.2), and very high pressure (jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:milog</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:miP</mml:mi> mml:mrow <mml:mo stretchy="true">/</mml:mo> </mml:mrow> mml:mik</mml:mi> <mml:mo stretchy="false">)</mml:mo> mml:mo≃</mml:mo> mml:mn8</mml:mn> mml:mo−</mml:mo> mml:mn9</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjacba8aieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, units of cmjats:sup−3</jats:sup>). The combination of [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>4364/Hjats:italicγ</jats:italic> and [O jats:sciii</jats:sc>]jats:italicλ</jats:italic>(4960 + 5008)/Hjats:italicβ</jats:italic> line ratios indicate very high electron temperatures of jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn4.1</mml:mn> mml:mo<</mml:mo> mml:milog</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:msub mml:mrow mml:miT</mml:mi> </mml:mrow> mml:mrow mml:mie</mml:mi> </mml:mrow> </mml:msub> mml:mrow <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> <mml:mo stretchy="false">)</mml:mo> mml:mo<</mml:mo> mml:mn4.4</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjacba8aieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, further implying metallicities of jats:italicZ</jats:italic>/jats:italicZ</jats:italic> jats:sub⊙</jats:sub> ≲ 0.2 with the application of low-redshift calibrations for “jats:italicT</jats:italic> jats:sub jats:italice</jats:italic> </jats:sub>-based” metallicities. These observations represent a tantalizing new view of the physical conditions of the ISM in galaxies at cosmic dawn.</jats:p>