  Supersoft X-ray sources (SSS) have been identified as white dwarfs accreting
from binary companions and undergoing nuclear-burning of the accreted material
on their surface. Although expected to be a relatively numerous population from
both binary evolution models and their identification as Type Ia supernova
progenitor candidates, given the very soft spectrum of SSSs relatively few are
known. Here we report on the X-ray and optical properties of 1RXS
J050526.3-684628, a previously unidentified accreting nuclear-burning white
dwarf located in the Large Magellanic Cloud (LMC). XMM-Newton observations
enabled us to study its X-ray spectrum and measure for the first time short
period oscillations of ~170 s. By analysing newly obtained X-ray data by
eROSITA, together with Swift observations and archival ROSAT data, we have
followed its long-term evolution over the last 3 decades. We identify 1RXS
J050526.3-684628 as a slowly-evolving post-nova SSS undergoing residual surface
nuclear-burning, which finally reached its peak in 2013 and is now declining.
Though long expected on theoretical grounds, such long-lived residual-burning
objects had not yet been found. By comparison with existing models, we find
that the effective temperature and luminosity evolution are consistent with a
~0.7 $M_{\odot}$ carbon-oxygen white dwarf accreting
~10$^{-9}~\rm{M}_{\odot}$/yr. Our results suggest there may be many more
undiscovered SSSs and "missed" novae awaiting dedicated deep X-ray searches in
the LMC and elsewhere.
