  Cosmic rays play a pivotal role in launching galactic winds, particularly in
quiescently star-forming galaxies where the hot gas alone is not sufficient to
drive a wind. Except for the Milky Way, not much is known about the transport
of cosmic rays in galaxies. In this Letter, we present low-frequency
observations of the nearby edge-on spiral galaxy NGC 4565 using the
LOw-Frequency ARray (LOFAR). With our deep 144-MHz observations, we obtain a
clean estimate of the emission originating from old cosmic-ray electrons (CRe),
which is almost free from contamination by thermal emission. We measured
vertical profiles of the non-thermal radio continuum emission that we fitted
with Gaussian and exponential functions. The different profile shapes
correspond to 1D cosmic-ray transport models of pure diffusion and advection,
respectively. We detect a warp in the radio continuum that is reminiscent of
the previously known HI warp. Because the warp is not seen at GHz-frequencies
in the radio continuum, its minimum age must be about 100 Myr. The warp also
explains the slight flaring of the thick radio disc that can otherwise be well
described by a Gaussian profile with an FWHM of 65 arcsec (3.7 kpc). The
diffusive radio halo together with the extra-planar X-ray emission may be
remnants of enhanced star-forming activity in the past where the galaxy had a
galactic wind, as GHz-observations indicate only a weak outflow in the last 40
Myr. NGC 4565 could be in transition from an outflow- to an inflow-dominated
phase.
