Coherent radio bursts detected from M dwarfs have some analogy with solar radio bursts, but reach orders of magnitude higher luminosities. These events trace particle acceleration, powered by magnetic reconnection, shock fronts (such as formed by coronal mass ejections, CMEs), and magnetospheric currents, in some cases offering the only window into these processes in stellar atmospheres. We conducted a 58-hour, ultra-wideband survey for coherent radio bursts on 5 active M dwarfs. We used the Karl G. Jansky Very Large Array (VLA) to observe simultaneously in three frequency bands covering a subset of 224-482 MHz and 1-6 GHz, achieving the widest fractional bandwidth to date for any observations of stellar radio bursts. We detected 22 bursts across 13 epochs, providing the first large sample of wideband dynamic spectra of stellar coherent radio bursts. The observed bursts have diverse morphology, with durations ranging from seconds to hours, but all share strong (40-100%) circular polarization. No events resemble solar Type II bursts (often associated with CMEs), but we cannot rule out the occurrence of radio-quiet stellar CMEs. The hours-long bursts are all polarized in the sense of the x-mode of the star's large-scale magnetic field, suggesting they are cyclotron maser emission from electrons accelerated in the large-scale field, analogous to auroral processes on ultracool dwarfs. The duty cycle of luminous coherent bursts peaks at 25% at 1-1.4 GHz, declining at lower and higher frequencies, indicating source regions in the low corona. At these frequencies, active M dwarfs should be the most common galactic transient source.