  We present a pioneering spatially-resolved, multi-phase gas abundance study
on the blue compact dwarf galaxy NGC~5253, targeting 10 star-forming (SF)
clusters inside six FUV HST/COS pointings with co-spatial optical VLT/MUSE
observations throughout the galaxy. The SF regions span a wide range of ages
(1--15 Myr) and are distributed at different radii (50 -- 230 pc). We performed
robust absorption-line profile fitting on the COS spectra, covering 1065--1430
\AA\ in the FUV, allowing an accurate computation of neutral-gas abundances for
13 different ions sampling 8 elements. These values were then compared with the
ionized-gas abundances, measured using the direct method on MUSE integrated
spectra inside analog COS apertures. Our multi-phase, spatially resolved
comparisons find abundances which are lower in the neutral gas than the ionized
gas by 0.22 dex, 0.80 dex and 0.58 dex for log(O/H), log(N/H) and log(N/O),
respectively. We modeled the chemical abundance distributions and evaluated
correlations as a function of radius and age. It was found that while N, O and
N/O abundances decrease as a function of age in the ionized gas, they increase
with age in the neutral gas. No strong correlations for N, O or N/O were
observed as a function of radius. The N/O and N/H offsets between the phases
were found to decrease with age, providing evidence that chemical enrichment
happens differentially, first in the ionized-gas phase around 2--5 Myrs (due to
N-rich Wolf-Rayet stars) and then mixing out into the cold neutral gas on
longer timescales of 10--15 Myr.
