  We report the observation of a fully developed fractional quantum Hall state
at $\nu=5/2$ in GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells with mobility well
below $10^{7}$\thinspace cm$^{2}$/Vs. This is achieved either by strong
illumination or reducing the barrier Al composition without illumination. We
explain both results in terms of screening of the ionized remote impurity (RI)
potential by nearby neutral shallow donors. Despite the dramatic improvement in
the transport features, the energy gap $\Delta_{5/2}$ is limited to a rather
small value ($\sim100$ mK), which indicates that once the RI potential is well
screened and the $5/2$ state emerges, the size of $\Delta_{5/2}$ is limited by
the mobility, i.e., by background impurities.
