  We reconsider our former determination of the chiral quark condensate
$\langle \bar q q \rangle$ from the related QCD spectral density of the
Euclidean Dirac operator, using our Renormalization Group Optimized
Perturbation (RGOPT) approach. Thanks to the recently available {\em complete}
five-loop QCD RG coefficients, and some other related four-loop results, we can
extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to
$N^5LO$ (six-loops), the latter within a well-defined approximation accounting
for all six-loop contents exactly predictable from five-loops RG properties.
The RGOPT results overall show a very good stability and convergence, giving
primarily the RG invariant condensate, $\langle \bar q
q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \bar\Lambda_0 $,
$\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019})
\bar\Lambda_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) =
-(0.751_{-.010}^{+0.019}) \bar\Lambda_3 $, where $\bar\Lambda_{n_f}$ is the
basic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and the
range spanned is our rather conservative estimated theoretical error. This
leads {\it e.g.} to $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) =
-(273^{+7}_{-4}\pm 13)$ MeV, using the latest $\bar\Lambda_3$ values giving the
second uncertainties. We compare our results with some other recent
determinations. As a by-product of our analysis we also provide complete
five-loop and partial six-loop expressions of the perturbative QCD spectral
density, that may be useful for other purposes.
