An investigation of the torsion-rotation-vibration energies in the ν 5 vibrational state in CH 3 CF 3 has been carried out using infrared and mm-wave spectroscopy. The lowest frequency parallel fundamental band ν 5 near 600 cm -1 has been measured at a resolution of 0.00125 cm -1 with Fourier transform spectroscopy for the two lowest torsional states v 6 = 0 and 1. The cold band (v 5 = 1, v 6 = 0) ← (v 5 = 0, v 6 = 0) showed no torsional splittings and looked much like a parallel band in a C 3v molecule. The hot band (v 5 = 1, v 6 = 1) ← (v 5 = 0, v 6 = 1) consisted of three distinct subbands, one for each torsional sublevel σ = 0, +1, and -1. For the state (v 5 = 1, v 6 = 1), the torsional splitting was increased from ∼0.001 cm -1 to ∼0.022 cm -1 by torsion-mediated Fermi-type interaction primarily with the dark state (v 5 = 0, v 6 = 5). The effects of this coupling on the spectrum are striking in spite of the fact that the two interacting states are ∼100 cm -1 apart and differ by four units in v 6 . The large amplitude character of the state (v 5 = 0, v 6 = 5) is seen to be largely responsible for the unusual (k, σ ) dependence of the energies in the state (v 5 = 1, v 6 = 1). The pure rotational spectrum in the state (v 5 = 1, v 6 = 0) has been measured between ∼50 and 370 GHz with Doppler-limited resolution; no σ -splitting was detected. The 3590 infrared and mm-wave frequencies measured here have been analyzed together with the 1494 measurements reported earlier by Wang et al. in an analysis of the vibrational ground state (2001, J. Mol. Spectrosc. 205, 146-163). A good fit was obtained here by varying 36 parameters in a Hamiltonian which takes into account the interaction between the torsional stacks of levels for v 5 = 0 and 1, as well as the (A 1 -A 2 ) splittings measured earlier for v 5 = 0. The explicit treatment of the interstack interactions is shown to lead to significant changes in the parameters (V 0,3 , V 0,6 ) that characterize the torsional potential for v 5 = 0. These changes have been explained quantitatively by examining the contact transformation that is implicitly applied when the interstack coupling is neglected.