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Resistive switching is of the key phenomena for applications such as nonvolatile memories or neuromorphic computing. V_{3}O_{5}, a compound of the vanadium oxide Magnéli series, is one of the rare materials to exhibit an insulator-metal transition above room temperature (T_{c}∼415 K). The switching mechanisms in this material are still not clear. Here, we demonstrate both static dc volatile resistive switching and fast oscillatory spiking regimes in V_{3}O_{5} devices at room temperature (120 K below the phase transition temperature) by applying an electric field. We couple electrical measurements, operando optical imaging, and infrared measurements to track the reflectivity change and the temperature of a device during the resistive switching. We find that the resistive switching starts via thermal runaway deep in the insulating state and triggers the phase transition with the formation of a filament of the high-temperature phase. Furthermore, we capture optically and thermally the spiking oscillations that we link to the negative differential resistance regime and find the filament forms and dissolves via a periodic spatiotemporal instability that we describe by numerical simulations. Our studies play an important role in understanding the volatile resistive switching mechanisms and demonstrate that V_{3}O_{5} can be a key vanadium oxide for neuromorphic computing.