  We measure the current expansion rate of the Universe, Hubble's constant
$H_0$, by calibrating the absolute magnitudes of supernovae to distances
measured by Baryon Acoustic Oscillations. This `inverse distance ladder'
technique provides an alternative to calibrating supernovae using nearby
absolute distance measurements, replacing the calibration with a high-redshift
anchor. We use the recent release of 1829 supernovae from the Dark Energy
Survey spanning $0.01\lt z \lt1.13$ anchored to the recent Baryon Acoustic
Oscillation measurements from DESI spanning $0.30 \lt z_{\mathrm{eff}} \lt
2.33$. To trace cosmology to $z=0$, we use the third-, fourth- and fifth-order
cosmographic models, which, by design, are agnostic about the energy content
and expansion history of the universe. With the inclusion of the
higher-redshift DESI-BAO data, the third-order model is a poor fit to both data
sets, with the fourth-order model being preferred by the Akaike Information
Criterion. Using the fourth-order cosmographic model, we find
$H_0=67.19^{+0.66}_{-0.64}\mathrm{~km} \mathrm{~s}^{-1} \mathrm{~Mpc}^{-1}$, in
agreement with the value found by Planck without the need to assume
Flat-$\Lambda$CDM. However the best-fitting expansion history differs from that
of Planck, providing continued motivation to investigate these tensions.
