Electron-capture cross sections in collisions of ${\mathrm{N}}^{4+}$ ions with atomic hydrogen is studied using the close-coupling two-center atomic orbital expansion method by treating the collision system in a quasi-two-electron model. Total electron-capture cross sections to the dominant individual singlet and triplet excited states are evaluated over the energy range of 50--20 000 eV/amu. The results are compared to existing experimental data and to theoretical calculations based on the molecular orbital expansion method. It is found that while the general overall agreement is satisfactory, the large experimental uncertainty cannot be used to discriminate the different theories. For the present energy range our results are closer to the semiclassical close coupling calculations based on the molecular orbital expansion method of Shimakura et al. [Phys. Rev. A 45, 267 (1993)] than the quantum calculations of Zygelman et al. [Phys. Rev. A 56, 457 (1997)].