  We consider $5$ dimensional electrostatic solutions to Einstein-Maxwell
gravity with $2$ commuting spacelike Killing fields. Taking two distinct
reductions from $5$ dimensions to a $3$ dimensional base space, we write the
Einstein-Maxwell equations using some axially symmetric functions on
$\mathbb{R}^3$. These equations can be viewed as arising from a harmonic map
coupled to 3-dimensional gravity with the isometries of the target space of
this map revealing a hidden $SL(2,\mathbb{R})$ symmetry of this sector of the
theory. Depending on the choice of reduction this symmetry then gives rise to
two different 1-parameter families of transformations corresponding to either
charging a black hole or immersing it in a background electric field. We use
these transformations to charge a static black Saturn and a static $L(n,1)$
black lens spacetime and by tuning the strength of the external field, we cure
the conical singularities to give new regular solutions. Notably the
electrified black lens generated is the first example of a regular black lens
in Einstein-Maxwell gravity with topologically trivial asymptotics.
