  We numerically simulate the past tidal evolution of the five large moons of
Uranus (Miranda, Ariel, Umbriel, Titania, and Oberon). We find that the most
recent major mean-motion resonance (MMR) between any two moons, the
Ariel-Umbriel 5:3 MMR, had a large effect on the whole system. Our results
suggest that this resonance is responsible for the current 4.3$^{\circ}$
inclination of Miranda (instead of previously proposed 3:1 Miranda-Umbriel
MMR), and that all five moons had their inclinations excited during this
resonance. Miranda experienced significant tidal heating during the
Ariel-Umbriel 5:3 MMR due to its eccentricity being excited by Ariel's secular
perturbations. This tidal heating draws energy from shrinking of Miranda's
orbit, rather than Ariel's outward evolution, and can generate heat flows in
excess of 100 mW m$^{-2}$, sufficient to produce young coronae on Miranda. We
find that this MMR was followed by a sequence of secular resonances, which
reshuffled the moons' eccentricities and inclinations. We also find that the
precession of Oberon's spin axis is close to a resonance with the precession of
Umbriel's orbital plane, and that this spin-orbit resonance was likely excited
during the Ariel-Umbriel 5:3 MMR. After the exit from the MMR, subsequent
Ariel-Umbriel secular resonance and Oberon-Umbriel spin-orbit resonance may be
able to explain the current low inclinations of Ariel and Umbriel. The age of
Miranda's surface features tentatively suggests Uranian tidal
$Q=15,000-20,000$, which can be further refined in future work.
