We report elastic and rotationally inelastic cross sections for e(-)-XH3 collisions (X: N, P, As, Sb) at the static-exchange level of approximation. The energy range was from 7.5 up to 30 eV. Our fixed-nuclei scattering amplitudes were obtained through the Schwinger multichannel method with pseudopotentials (SMCPP) [M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Phys. Rev. A 47, 1111 (1993)]. The rotational cross sections were obtained with the help of the adiabatic-nuclei-rotation approximation. There is good agreement with available experimental elastic cross sections. In order to improve rotational cross sections at small scattering angles for the dipole-allowed 00-->10 rotational excitation, we have combined the SMCPP and the first Born approximation of the full interaction potential and also of the dipole moment potential. To our knowledge this is the first time that rotational excitation cross sections for these molecules are reported.