The effect of violation of \(T\)-invariance, provided that \(P\)-parity is preserved, is given by the total cross section of the interaction of a vector-polarized particle with a tensor-polarized target. A formalism for calculating this effect developed previously and based on the spin-dependent Glauber theory of elastic \(pd\) scattering is used here to calculate the effect under discussion in the range of collision energies corresponding to the invariant mass of the \(pN\) system \(\sqrt{s_{pN}}=5\)--\(30\) GeV. The spin-dependent amplitudes of elastic \(pN\) scattering required for this calculation are taken from existing phenomenological models for \(pN\) scattering in the energy region considered.