  The fact that neutrinos carry a non-vanishing rest mass is evidence of
physics beyond the Standard Model of elementary particles. Their absolute mass
bears important relevance from particle physics to cosmology. In this work, we
report on the search for the effective electron antineutrino mass with the
KATRIN experiment. KATRIN performs precision spectroscopy of the tritium
$\beta$-decay close to the kinematic endpoint. Based on the first five
neutrino-mass measurement campaigns, we derive a best-fit value of $m_\nu^{2} =
{-0.14^{+0.13}_{-0.15}}~\mathrm{eV^2}$, resulting in an upper limit of $m_\nu <
{0.45}~\mathrm{eV}$ at 90 % confidence level. With six times the statistics of
previous data sets, amounting to 36 million electrons collected in 259
measurement days, a substantial reduction of the background level and improved
systematic uncertainties, this result tightens KATRIN's previous bound by a
factor of almost two.
