In the recent years, Slater-type geminals (STGs) have been used with great success to expand the first-order wave function in an explicitly-correlated perturbation theory. The present work reports on this theory's implementation in the framework of the Turbomole suite of programs. A formalism is presented for evaluating all of the necessary molecular two-electron integrals by means of the Obara-Saika recurrence relations, which can be applied when the STG is expressed as a linear combination of a small number (n) of Gaussians (STG-nG geminal basis). In the Turbomole implementation of the theory, density fitting is employed and a complementary auxiliary basis set (CABS) is used for the resolution-of-the-identity (RI) approximation of explicitly-correlated theory. By virtue of this RI approximation, the calculation of molecular three- and four-electron integrals is avoided. An approximation is invoked to avoid the two-electron integrals over the commutator between the operators of kinetic energy and the STG. This approximation consists of computing commutators between matrices in place of operators. Integrals over commutators between operators would have occurred if the theory had been formulated and implemented as proposed originally. The new implementation in Turbomole was tested by performing a series of calculations on rotational conformers of the alkanols n-propanol through n-pentanol. Basis-set requirements concerning the orbital basis, the auxiliary basis set for density fitting and the CABS were investigated. Furthermore, various (constrained) optimizations of the amplitudes of the explicitly-correlated double excitations were studied. These amplitudes can be optimized in orbital-variant and orbital-invariant manners, or they can be kept fixed at the values governed by the rational generator approach, that is, by the electron cusp conditions. Electron-correlation effects beyond the level of second-order perturbation theory were accounted for by conventional coupled-cluster calculations with single, double and perturbative triple excitations [CCSD(T)]. The explicitly-correlated perturbation theory results were combined with CCSD(T) results and compared with literature data obtained by basis-set extrapolation.