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Efficient chirped pulse amplification of broadband mid-IR (4-5 um) femtosecond seed pulse (230 ps, 4uJ) generated in AgGaS2 based OPA driven by Cr:forsterite laser in multi-pass Fe2+:ZnSe amplifier optically pumped by solid-state Q-switched Cr:Yb:Ho:YSGG laser (2.85 um, 30mJ, 5Hz, 0.6 J/cm^2) has been demonstrated. The hybrid system delivers 2.1 mJ at pulse duration of 230-ps. Straightforward compression to 150 fs pulse is achievable with 70% efficiency using diffraction grating pair with peak power of about 10.5 GW. Further grating based and non-linear compression in a bulk CaF2 due to the SPM and anomalous GVD should provide the enhancement of peak power up to 35 GW. Possible routes to reach sub-TW and even TW power level in mid-IR are discussed.