Analytical-expressions of the fourth and the fifth virial coefficients for the dipole hard sphere fluid in zero external magnetic field are obtained on the basis of numerical results of Mayer-sampling calculations. The virial coefficients are incorporated in to the so-called logarithmic free energy (LFE) theory [E.A. Elfimova, A.O. Ivanov, P.J. Camp, Phys. Rev. E, 86, 021126 (2012)]. In this theory, the virial expansion of the Helmholtz free energy is re-summed into a logarithmic function. The argument of the logarithm is a polynomial expansion in density with coefficients chosen to give the first few terms in the conventional virial expansion. The theoretical predictions of the thermodynamic functions based on the LFE theory that accounts five virial coefficients are compared critically with published results from Monte Carlo simulations, conventional virial expansion, and known theory based on Fade approximation [G.S. Rushbrooke, G. Steil, J.S. Hoye, Mol. Phys., 26, 1199 (1973)]. It is shown that the LFE theory accurately captures computer simulation results for dipolar coupling constant lambda <= 4, even at the highest value of the particle volume fraction phi less than or similar to 0.5, and outperforms thermodynamic theories mentioned above. (C) 2016 Elsevier B.V. All rights reserved.