We present observations and detailed characterizations of five new host galaxies of fast radio bursts (FRBs) discovered with the Australian Square Kilometre Array Pathfinder (ASKAP) and localized to $lesssim 1$. Combining these galaxies with FRB hosts from the literature, we introduce criteria based on the probability of chance coincidence to define a sub-sample of 10 highly-confident associations (at $z=0.03-0.52$), three of which correspond to known repeating FRBs. Overall, the FRB host galaxies exhibit a broad, continuous range of color ($M_u-M_r = 0.9 - 2.0$), stellar mass ($M_star = 10^{8} - 6times 10^{10},M_{odot}$), and star-formation rate (${rm SFR} = 0.05 - 10,M_{odot},{rm yr}^{-1}$) spanning the full parameter space occupied by $z<0.5$ galaxies. However, they do not track the color-magnitude, SFR-$M_star$, nor BPT diagrams of field galaxies surveyed at similar redshifts. There is an excess of green valley galaxies and an excess of emission-line ratios indicative of a harder radiation field than that generated by star-formation alone. From the observed stellar mass distribution, we rule out the hypothesis that FRBs strictly track stellar mass in galaxies ($>99%$ c.l.). We measure a median offset of 3.3 kpc from the FRB to the estimated center of the host galaxies and compare the host-burst offset distribution and other properties with the distributions of long- and short-duration gamma-ray bursts (LGRBs and SGRBs), core-collapse supernovae (CC-SNe), and Type Ia SNe. This analysis rules out galaxies hosting LGRBs (faint, star-forming galaxies) as common hosts for FRBs ($>95%$ c.l.). Other transient channels (SGRBs, CC- and Type Ia SNe) have host galaxy properties and offsets consistent with the FRB distributions. All of the data and derived quantities are made publicly available on a dedicated website and repository.
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