  We present a volume-limited, spectroscopically-verified sample of M7$-$L5
ultracool 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 be
M7$-$L5 dwarfs within 25\,pc when distance or spectral type uncertainties are
taken into account. The spectra provide NIR spectral and gravity
classifications, and we use these to identify young sources, red and blue
$J-K_S$ color outliers, and spectral binaries. We measure very low gravity and
intermediate gravity fractions of $2.1^{+0.9}_{-0.8}\%$ and
$7.8^{+1.7}_{-1.5}\%$, respectively; fractions of red and blue color outliers
of $1.4^{+0.6}_{-0.5}$\% and $3.6^{+1.0}_{-0.9}$\%, respectively; and a
spectral binary fraction of $1.6^{+0.5}_{-0.5}\%$. We present an updated
luminosity function for M7$-$L5 dwarfs continuous across the hydrogen burning
limit that agrees with previous studies. We estimate our completeness to range
between $69-80\%$ when compared to an isotropic model. However, we find that
the literature late-M sample is severely incomplete compared to L dwarfs, with
completeness of $62^{+8}_{-7}\%$ and $83^{+10}_{-9}\%$, respectively. This
incompleteness can be addressed with astrometric-based searches of ultracool
dwarfs with \textit{Gaia} to identify objects previously missed by color- and
magnitude-limited surveys.

Solar and Stellar Astrophysics