We report the single-crystal growth of the noncentrosymmetric cubic heavy-fermion paramagnet UPt5 and comparative Fermi surface studies of de Haas-van Alphen (dHvA) experiments and theoretical band calculations. We also present the results of single-crystal x-ray diffraction, electrical resistivity, heat capacity, and magnetization measurements using single crystals of UPt5. The dHvA experiments reveal nearly spherical split hole Fermi surfaces and largely split electron Fermi surfaces, which are in agreement with the results of a band-structure calculation. The largely split electron Fermi surfaces may be understood through the antisymmetric spin-orbit interaction derived from U-5f and Pt-5d electrons. We explain the observed unexpected dHvA frequencies quasiquantitatively based on orbital crossing using the coupled network analysis in the split hole Fermi surface pair. Furthermore, the temperature dependence of the dHvA amplitude reveals enhanced cyclotron effective masses of up to 29m0 and a peculiar anisotropic effective mass in the paramagnetic cubic heavy-fermion UPt5.