  The interstellar and intra-cluster medium in giant elliptical galaxies and
clusters of galaxies is often assumed to be in hydrostatic equilibrium.
Numerical simulations, however, show that about 5-30% of the pressure in a
cluster is provided by turbulence induced by, for example, the central AGN and
merger activity. We aim to put constraints on the turbulent velocities and
turbulent pressure in the ICM of the giant elliptical galaxies NGC 5044 and NGC
5813 using XMM-Newton RGS observations. The magnitude of the turbulence is
estimated using the Fe XVII lines at 15.01 A, 17.05 A, and 17.10 A in the RGS
spectra. At low turbulent velocities, the gas becomes optically thick in the
15.01 A line due to resonant scattering, while the 17 A lines remain optically
thin. By comparing the (I(17.05)+I(17.10))/I(15.01) line ratio from RGS with
simulated line ratios for different Mach numbers, the level of turbulence is
constrained. The measurement is limited by systematic uncertainties in the
atomic data, which are at the 20-30% level. We find that the line ratio in NGC
5813 is significantly higher than in NGC 5044. This difference can be explained
by a higher level of turbulence in NGC 5044. The high turbulent velocities and
the fraction of the turbulent pressure support of >40% in NGC 5044, assuming
isotropic turbulence, confirm that it is a highly disturbed system, probably
due to an off-axis merger. The turbulent pressure support in NGC 5813 is more
modest at 15-45%. The (I(17.05)+I(17.10))/I(15.01) line ratio in an optically
thin plasma, calculated using AtomDB v2.0.1, is 2 sigma above the ratio
measured in NGC 5044, which cannot be explained by resonant scattering. This
shows that the discrepancies between theoretical, laboratory, and astrophysical
data on Fe XVII lines need to be reduced to improve the accuracy of the
determination of turbulent velocities using resonant scattering.
