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We reconsider our former determination of the chiral quark condensate$\langle \bar q q \rangle$ from the related QCD spectral density of theEuclidean Dirac operator, using our Renormalization Group OptimizedPerturbation (RGOPT) approach. Thanks to the recently available {\em complete}five-loop QCD RG coefficients, and some other related four-loop results, we canextend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to$N^5LO$ (six-loops), the latter within a well-defined approximation accountingfor all six-loop contents exactly predictable from five-loops RG properties.The RGOPT results overall show a very good stability and convergence, givingprimarily the RG invariant condensate, $\langle \bar qq\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 thebasic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and therange spanned is our rather conservative estimated theoretical error. Thisleads {\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 thesecond uncertainties. We compare our results with some other recentdeterminations. As a by-product of our analysis we also provide completefive-loop and partial six-loop expressions of the perturbative QCD spectraldensity, that may be useful for other purposes.

Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation