  The soft X-ray pulsar RX J1856.5-3754 is the brightest member of a small
class of thermally-emitting, radio-silent, isolated neutron stars. Its X-ray
spectrum is almost indistinguishable from a blackbody with $kT^\infty\approx
60$ eV, but evidence of harder emission above $\sim 1$ keV has been recently
found. We report on a spectral and timing analysis of RX J1856.5-3754 based on
the large amount of data collected by XMM-Newton in 2002--2022, complemented by
a dense monitoring campaign carried out by NICER in 2019. Through a
phase-coherent timing analysis we obtained an improved value of the spin-down
rate $\dot{\nu}=-6.042(4)\times10^{-16}$ Hz s$^{-1}$, reducing by more than one
order magnitude the uncertainty of the previous measurement, and yielding a
characteristic spin-down field of $1.47\times10^{13}$ G. We also detect two
spectral components above $\sim1$ keV: a blackbody-like one with
$kT^\infty=138\pm13$ eV and emitting radius $31_{-16}^{+8}$ m, and a power law
with photon index $\Gamma=1.4_{-0.4}^{+0.5}$. The power-law 2--8\,keV flux,
$(2.5_{-0.6}^{+0.7})\times10{-15}$ erg cm$^{-2}$ s$^{-1}$, corresponds to an
efficiency of $10^{-3}$, in line with that seen in other pulsars. We also
reveal a small difference between the $0.1$--$0.3$ keV and $0.3$--$1.2$ keV
pulse profiles, as well as some evidence for a modulation above $1.2$ keV.
These results show that, notwithstanding its simple spectrum, \eighteen still
has a non-trivial thermal surface distribution and features non-thermal
emission as seen in other pulsars with higher spin-down power.
