The molecular gas content of high-redshift galaxies is a highly sought-after property. However, H2 is not directly observable in most environments, so its mass is probed through other emission lines (e.g., CO, [CI], [CII]), or through a gas-to-dust ratio. Each of these methods depends on several assumptions, and are best used in parallel. In this work, we extend an additional molecular gas tracer to high-redshift studies by observing hydrogen deuteride (HD) emission in the strongly lensed z = 5.656 galaxy SPT0346-52 with ALMA. While no HD(1-0) emission is detected, we are able to place an upper limit on the gas mass of $\rm M_{H_2}<6.4\times 10^{11}\, M_{\odot }$. This is used to find a limit on the $L^{\prime }_{CO}$ conversion factor of $\rm \alpha _{CO}<5.8$ M⊙(K km s−1 pc2)−1. In addition, we construct the most complete spectral energy distribution (SED) of this source to date, and fit it with a single-temperature modified blackbody using the nested sampling code MultiNest, yielding a best-fit dust mass Mdust = 108.92 ± 0.02 M⊙, dust temperature 78.6 ± 0.5 K, dust emissivity spectral index β = 1.81 ± 0.03, and star formation rate SFR = 3800 ± 100 M⊙ year−1. Using the continuum flux densities to estimate the total gas mass of the source, we find M$_{H_2}<2.4\times 10^{11}$ M⊙, assuming sub-solar metallicity. This implies a CO conversion factor of αCO < 2.2, which is between the standard values for MW-like galaxies and starbursts. These properties confirm that SPT0346-52 is a heavily starbursting, gas rich galaxy.