  Eclipsing binary stars with an oscillating giant component allow accurate
stellar parameters to be derived and asteroseismic methods to be tested and
calibrated. To this aim, suitable systems need to be firstly identified and
secondly measured precisely and accurately. KIC 4054905 is one such system,
which has been identified, but with measurements of a relatively low precision
and with some confusion regarding its parameters and evolutionary state. Our
aim is to provide a detailed and precise characterisation of the system and to
test asteroseismic scaling relations. Dynamical and asteroseismic parameters of
KIC4054905 were determined from Kepler photometry and multi-epoch
high-resolution spectra from FIES at the Nordic Optical Telescope. KIC 4054905
was found to belong to the thick disk and consist of two lower red giant branch
(RGB) components with nearly identical masses of 0.95$M_{\odot}$ and an age of
$9.9\pm0.6$ Gyr. The most evolved star displays solar-like oscillations, which
suggest that the star belongs to the RGB, supported also by the radius, which
is significantly smaller than the red clump phase for this mass and
metallicity. Masses and radii from corrected asteroseismic scaling relations
can be brought into full agreement with the dynamical values if the RGB phase
is assumed, but a best scaling method could not be identified. We measured
dynamical masses and radii with a precision better than 1.0%. We firmly
establish the evolutionary nature of the system to be that of two early RGB
stars with an age close to 10 Gyr, unlike previous findings. The metallicity
and Galactic velocity suggest that the system belongs to the thick disk of the
Milky Way. We investigate the agreement between dynamical and asteroseismic
parameters for KIC 4054905. Consistent solutions exist, but the need to analyse
more systems continues in order to establish the accuracy of asteroseismic
methods.
