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We present a volume-limited, spectroscopically-verified sample of M7$-$L5ultracool dwarfs within 25\,pc. The sample contains 410 sources, of which$93\%$ have trigonometric distance measurements ($80\%$ from \textit{Gaia}DR2), and $81\%$ have low-resolution ($R\sim120$), near-infrared (NIR)spectroscopy. We also present an additional list of 60 sources which may beM7$-$L5 dwarfs within 25\,pc when distance or spectral type uncertainties aretaken into account. The spectra provide NIR spectral and gravityclassifications, and we use these to identify young sources, red and blue$J-K_S$ color outliers, and spectral binaries. We measure very low gravity andintermediate gravity fractions of $2.1^{+0.9}_{-0.8}\%$ and$7.8^{+1.7}_{-1.5}\%$, respectively; fractions of red and blue color outliersof $1.4^{+0.6}_{-0.5}$\% and $3.6^{+1.0}_{-0.9}$\%, respectively; and aspectral binary fraction of $1.6^{+0.5}_{-0.5}\%$. We present an updatedluminosity function for M7$-$L5 dwarfs continuous across the hydrogen burninglimit that agrees with previous studies. We estimate our completeness to rangebetween $69-80\%$ when compared to an isotropic model. However, we find thatthe literature late-M sample is severely incomplete compared to L dwarfs, withcompleteness of $62^{+8}_{-7}\%$ and $83^{+10}_{-9}\%$, respectively. Thisincompleteness can be addressed with astrometric-based searches of ultracooldwarfs with \textit{Gaia} to identify objects previously missed by color- andmagnitude-limited surveys.

The Ultracool SpeXtroscopic Survey. I. Volume-Limited Spectroscopic Sample and Luminosity Function of M7$-$L5 Ultracool Dwarfs