  Recent progress on robust clustering led to constant-factor approximations
for Robust Matroid Center. After a first combinatorial $7$-approximation that
is based on a matroid intersection approach, two tight LP-based
$3$-approximations were discovered, both relying on the Ellipsoid Method. In
this paper, we show how a carefully designed, yet very simple, greedy selection
algorithm gives a $5$-approximation. An important ingredient of our approach is
a well-chosen use of Rado matroids. This enables us to capture with a single
matroid a relaxed version of the original matroid, which, as we show, is
amenable to straightforward greedy selections.
