AM CVn systems are ultra-compact, hydrogen-depleted, and helium-rich, accreting binaries with degenerate or semidegenerate donors. We report the discovery of five new eclipsing AM CVn systems with orbital periods of 61.5, 55.5, 53.3, 37.4, and 35.4 min. These systems were discovered by searching for deep eclipses in the Zwicky Transient Facility (ZTF) light curves of white dwarfs selected using Gaia parallaxes. We obtained phase-resolved spectroscopy to confirm that all systems are AM CVn binaries, and we obtained high-speed photometry to confirm the eclipse and characterize the systems. The spectra show double-peaked H e lines but also show metals, including K and Zn, elements that have never been detected in AM CVn systems before. By modelling the high-speed photometry, we measured the mass and radius of the donor star, potentially constraining the evolutionary channel that formed these AM CVn systems. We determined that the average mass of the accreting white dwarf is ≍0.8 M⊙, and that the white dwarfs in long-period systems are hotter than predicted by recently updated theoretical models. The donors have a high entropy and are a factor of ≍2 more massive compared to zero-entropy donors at the same orbital period. The large donor radius is most consistent with H e-star progenitors, although the observed spectral features seem to contradict this. The discovery of five new eclipsing AM CVn systems is consistent with the known observed AM CVn space density and estimated ZTF recovery efficiency.