  We present a robust representation of the chemical and thermal structure in
the galaxy group NGC 5813 using archival, deep X-ray observations, and
employing a multi-temperature spectral model based on up to date atomic line
emission databases. The selection of our target is motivated by the fact that
NGC 5813 has a very relaxed morphology, making it a promising candidate for the
study of the AGN feedback's influence in the intra-group medium (IGrM). Our
results showcase a prominent, extended distribution of cool gas along the
group's NE-SW direction, correlating with the direction along which the
supermassive black hole in the group's central galaxy is known to interact with
the IGrM. Our analysis indicates gas being uplifted from the group's centre as
the probable origin of the cool gas, although alternative scenarios, such as
in-situ cooling can not be explicitly ruled out. Regarding the chemical
structure of the IGrM, and unlike previous findings in massive clusters, we
find no evidence for recent metal transport by jets/lobes from the central AGN.
Instead, elemental abundances remain near Solar on average across the group.
The distribution of elements appears to be independent of galactocentric
radius, azimuth and the thermodynamics of the gas, suggesting that the IGrM has
been efficiently mixed. The large scale uniformity of the abundance
distribution implies the presence of complex dynamical processes in NGC 5813,
despite its overall relaxed morphology. Past events of extreme AGN feedback or
sloshing could be the primary mechanisms behind this.
