  We present the confirmation of a hot super-Neptune with an exterior Neptune
companion orbiting a bright (V = 10.1 mag) F-dwarf identified by the
$\textit{Transiting Exoplanet Survey Satellite}$ ($\textit{TESS}$). The two
planets, observed in sectors 45, 46 and 48 of the $\textit{TESS}$ extended
mission, are $4.74^{+0.16}_{-0.14}$ $R_{\oplus}$ and $3.86^{+0.17}_{-0.16}$
$R_{\oplus}$ with $5.4588385^{+0.0000070}_{-0.0000072}$ d and
$17.8999^{+0.0018}_{-0.0013}$ d orbital periods, respectively. We also obtained
precise space based photometric follow-up of the system with ESAs
$\textit{CHaracterising ExOplanets Satellite}$ ($\textit{CHEOPS}$) to constrain
the radius and ephemeris of TOI-5126 b. TOI 5126 b is located in the "hot
Neptune Desert" and is an ideal candidate for follow-up transmission
spectroscopy due to its high predicted equilibrium temperature ($T_{eq} =
1442^{+46}_{-40}$ K) implying a cloud-free atmosphere. TOI-5126 c is a warm
Neptune ($T_{eq}= 971^{+31}_{-27}$ K) also suitable for follow-up. Tentative
transit timing variations (TTVs) have also been identified in analysis,
suggesting the presence of at least one additional planet, however this signal
may be caused by spot-crossing events, necessitating further precise
photometric follow-up to confirm these signals.
