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 ∗ = 108 - 6 × 1010 M o˙), and star formation rate (SFR = 0.05-10 M o˙ yr-1) spanning the full parameter space occupied by z < 0.5 galaxies. However, they do not track the color-magnitude, SFR-M ∗, 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.