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The virial expansion characterizes the high-temperature approach to thequantum-classical crossover in any quantum many-body system. Here, we calculatethe virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D,with attractive contact interactions, as relevant for a variety of applicationsin atomic and nuclear physics. To that end, we discretize the imaginary-timedirection and calculate the relevant canonical partition functions. In coarsediscretizations, we obtain analytic results featuring relationships between theinteraction-induced changes $\Delta b_3$, $\Delta b_4$, and $\Delta b_5$ asfunctions of $\Delta b_2$, the latter being exactly known in many cases byvirtue of the Beth-Uhlenbeck formula. Using automated-algebra methods, we pushour calculations to progressively finer discretizations and extrapolate to thecontinuous-time limit. We find excellent agreement for $\Delta b_3$ withprevious calculations in all dimensions and we formulate predictions for$\Delta b_4$ and $\Delta b_5$ in 1D and 2D. We also provide, for a range ofcouplings,the subspace contributions $\Delta b_{31}$, $\Delta b_{22}$, $\Deltab_{41}$, and $\Delta b_{32}$, which determine the equation of state and staticresponse of polarized systems at high temperature. As a performance check, wecompare the density equation of state and Tan contact with quantum Monte Carlocalculations, diagrammatic approaches, and experimental data where available.Finally, we apply Pad\'e and Pad\'e-Borel resummation methods to extend theusefulness of the virial coefficients to approach and in some cases go beyondthe unit-fugacity point.

The virial expansion of attractively interacting Fermi gases in 1D, 2D, and 3D, up to fifth order