  We report on the characterisation of the dust activity and dynamical
evolution of two faint active asteroids, P/2019 A4, and P/2021 A5, observed
with the 10.4m GTC using both imaging and spectroscopy. Asteroid P/2019 A4
activity is found to be linked to an impulsive event occurring some $\pm$10
days around perihelion, probably due to a collision or a rotational disruption.
Its orbit is stable over 100 Myr timescales. Dust tail models reveal a
short-term burst producing (2.0$\pm$0.7)$\times$10$^6$ kg of dust for maximum
particle radius rmax=1 cm. The spectrum of P/2019 A4 is featureless, and
slightly redder than the Sun. P/2021 A5 was active $\sim$50 days after
perihelion, lasting $\sim$5 to $\sim$60 days, and ejecting
(8$\pm$2)$\times$10$^6$ kg of dust for rmax=1 cm. The orbital simulations show
that a few percent of dynamical clones of P/2021 A5 are unstable on 20-50 Myr
timescales. Thus, P/2021 A5 might be an implanted object from the JFC region or
beyond. These facts point to water ice sublimation as the activation mechanism.
This object also displays a featureless spectrum, but slightly bluer than the
Sun. Nuclei sizes are estimated in the few hundred meters range for both
asteroids. Particle ejection speeds ($\sim$0.2 m/s) are consistent with escape
speeds from those small-sized objects.
