A five-wavelength-switchable thulium-doped fiber laser with a fiber Bragg grating (FBG)-based five-channel transmitting Fabry-Pérot (F-P) filter and a multi-coupler based triple-ring cavity (CTRC) filter, is experimentally proposed. For the first time, a multi-channel F-P filter and specially-designed coupler-based compound cavity filter were combined to realize multi-wavelengthswitchable operation, with single-longitudinal-mode (SLM) lasing for each wavelength channel in a 2 µm band fiber laser. The theoretical analysis of the CTRC filter and the principle for achieving SLM operation by corporately using the F-P filter and CTRC filter were presented in detail. The experimental results demonstrated the good performance of the proposed filters. Five lasing wavelengths (1941.13 nm, 1941.22 nm, 1941.30 nm, 1941.39 nm, and 1941.47 nm) were obtained with good switchability, and each operated in a stable SLM state. The OSNR of each lasing wavelength was higher than 50 dB, and the linewidths of all obtained wavelengths were less than 8 kHz.