Galaxy Clusters Selected via the Sunyaev-Zel'dovich Effect in 5 year data from the SPT-3G Main Survey

We report a new galaxy cluster catalog, selected using the thermal Sunyaev-Zel'dovich (SZ) effect, from 5 years of observations of the SPT-3G Main field. Drawn from arcminute-resolution data with white noise levels of 3.2, 2.5, and 8.9 $\mu$K-arcmin at 95, 150, and 220 GHz, respectively, the sample consists of 8,892 cluster candidates detected above significance $\xi=4$, with an expected purity of $>82\%$ (4,480 at $\xi\ge5$ with purity $>99\%$). Using optical and infrared data we have confirmed 7,190 candidates as clusters. The sample spans a mass range $7.9 \times 10^{13}$ $M_\odot/h_{70}$ \ $< M_\textrm{500c} < $ $1.6 \times 10^{15}$ $M_\odot/h_{70}$ with a median mass of $1.65 \times 10^{14}$ $M_\odot/h_{70}$, and a redshift range of $0.037<z\lesssim 2$ with a median redshift of $z_{\textrm{med}}$ = 0.73; 1,780 clusters are at $z>1$ and 271 at $z>1.5$. Compared to previous SZ cluster samples from South Pole Telescope and Atacama Cosmology Telescope data, the SPT-3G sample is highly consistent in mass and redshift but is significantly deeper, with per-cluster detection signal-to-noise 2-4 times higher and a cluster density of 4.5 confirmed clusters/deg$^2$. We cross match with eRASS1 cluster and point source catalogs, finding 1,279 and 1,319 matches, respectively. The SPT and eROSITA cluster mass estimates are in relatively good agreement. We perform a series of validation checks using both internal data splits and comparisons to external samples. These tests show increasing correlated (dusty) emission with redshift, with a $\sim17\times$ larger 220 GHz temperature increment for clusters at $z\sim1.5$ than $z\sim0.25$, but only weak evidence for correlated synchrotron emission. Finally, a number of clusters are flagged as candidate strong gravitational lenses.