The Fourier transform spectrum of the vibration-rotational bands υ2 and υ5 of gaseous fluoromethane 13CH3F was measured at an unapodized resolution 0.0041 cm-1. Among the assigned lines, 102 belonged to the Δk = ±2 perturbation-allowed transitions to the doubly degenerate vibrational state v5 = 1. Combination differences were generated for the ground state of 13CH3F from the wavenumbers of the allowed and forbidden vibration-rotational transitions to the v5 = 1 level. They were used in a simultaneous least squares fit with the previously measured microwave, submillimeterwave, and far infrared transition frequencies of the pure rotational transitions in the ground state and with the combination differences generated from the allowed transitions to the v3 = 1 state of 13CH3F (Pracna, Klee, Winnewisser, Papoušek, Yen-Chu Hsu, and Hann-Sen Chen, J. Mol. Spectrosc.156, 217-226 (1992). This made it possible to determine precisely for the first time A0 and D0K for 13CH3F: A0 = (5.1824246 ± 0.0000015) cm-1, D0K = (70.912 ± 0.033) × 10-6 cm-1.