  At present, the main satellites of Uranus are not involved in any low order
mean motion resonance (MMR). However, owing to tides raised in the planet,
Ariel and Umbriel most likely crossed the 5/3 MMR in the past. Previous studies
on this resonance passage relied on limited time-consuming N-body simulations
or simplified models focusing solely on the effects of the eccentricity or the
inclination. In this paper, we aim to provide a more comprehensive view on how
the system evaded capture in the 5/3 MMR. For that purpose, we developed a
secular resonant two-satellite model with low eccentricities and low
inclinations, including tides using the weak friction model. By performing a
large number of numerical simulations, we show that capture in the 5/3 MMR is
certain if the initial eccentricities of Ariel, $e_1$, and Umbriel, $e_2$, are
related through $(e_1^2 + e_2^2)^{1/2} < 0.007$. Moreover, we observe that the
eccentricity of Ariel is the key variable to evade the 5/3 MMR with a high
probability. We determine that for $e_1 > 0.015$ and $e_2 < 0.01$, the system
avoids capture in at least 60\% of the cases. We also show that, to replicate
the currently observed system, the initial inclinations of Ariel and Umbriel
must lay within $I_1 \leq 0.05^{\circ}$ and $0.06^{\circ} \leq I_2 \leq
0.11^{\circ}$, respectively. We checked these results using a complete N-body
model with the five main satellites and did not observe any significant
differences.
