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 1″. Combining these galaxies with FRB hosts from the literature, we introduce criteria based on the probability of chance coincidence to define a subsample of 10 highly confident associations (at z=0.03-0.52), 3 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 å =10 8 −6×10 10 M e), and star formation rate (SFR=0.05-10 M e yr −1) spanning the full parameter space occupied by z<0.5 galaxies. However, they do not track the color-magnitude, SFR-M å , 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 SNe Ia. 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 SNe Ia) 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.