Current measurements show that the observed fraction of Compton-thick (CT) AGN is smaller than the expected values needed to explain the cosmic X-ray background. Prior fits to the X-ray spectrum of the nearby Seyfert-2 galaxy NGC 5347 ($z=0.00792,, D =35.5 rm ~Mpc $) have alternately suggested a CT and Compton-thin source. Combining archival data from $Suzaku$, $Chandra$, and - most importantly - new data from $NuSTAR$, and using three distinct families of models, we show that NGC 5347 is an obscured CTAGN ($N_{rm H} > 2.23times 10^{24}~rm cm^{-2}$). Its 2-30~keV spectrum is dominated by reprocessed emission from distant material, characterized by a strong Fe K$alpha$ line and a Compton hump. We found a large equivalent width of the Fe K$alpha$ line ($rm EW = 2.3 pm 0.3$ keV) and a high intrinsic-to-observed flux ratio ($sim 100$). All of these observations are typical for bona fide CTAGN. We estimate a bolometric luminosity of $L_{rm bol} simeq 0.014 pm 0.005~L_{rm Edd.}$. The $Chandra$ image of NGC 5347 reveals the presence of extended emission dominating the soft X-ray spectrum ($E < 2,rm keV$), which coincides with the [O III] emission detected in the $Hubble ~Space~ Telescope$ images. Comparison to other CTAGN suggests that NGC 5347 is broadly consistent with the average properties of this source class. We simulated $XRISM$ and $Athena$/X-IFU spectra of the source, showing the potential of these future missions in identifying CTAGN in the soft X-rays.