We present data on the linear (transmission, index of refraction) and nonlinear (second-order susceptibility) optical properties of the quaternary semiconductor AgGaGe5Se12 with orthorhombic symmetry--a solid solution in the AgxGaxGe1-xSe2 system with x = 0.17. The nonlinear coefficients are estimated from phase-matched second-harmonic generation near 3 microm. After numerical analysis of the phase-matching configurations for three-wave nonlinear interactions, the first experimental results on difference-frequency mixing, producing tunable (4-7.5-microm) femtosecond pulses at a 1-kHz repetition rate, are described. The pulses of only five optical cycles (FWHM = 84 fs) are generated near 5 microm with energy of 0.5 microJ. Because of its higher damage threshold, larger birefringence and bandgap, and greater variety of phase-matching schemes, AgGaGe5Se12 could become an alternative to AgGaS2 and AgGaSe2, more widely used in high-power and specific applications.