A corner-pumped Nd:YAG/YAG composite slab continuous-wave laser operating at 1064 nm, 1074 nm, 1112 nm, 1116 nm, and 1123 nm simultaneously and a laser that is tunable at these wavelengths are reported for the first time. The maximum output power of the five-wavelength laser is 5.66 W with an optical-to-optical conversion efficiency of 11.3%. After a birefringent filter is inserted in the cavity, the five wavelengths can be separated successfully by rotating the filter. The maximum output powers of the 1064 nm, 1074 nm, 1112 nm, 1116 nm, and 1123 nm lasers are 1.51 W, 1.3 W, 1.27 W, 0.86 W, and 0.72 W, respectively.