Zintl compounds with the chemical formula Ca_(5)M_(2)Sb_6 have attracted attention as candidates for use in thermoelectric applications due to their low thermal conductivity and promising high temperature performance (i.e., zT = 0.6 at 1000 K in Ca_(5)Al_(2−x)Na_(x)Sb_6). We have shown previously that, relative to Ca_(5)Al_(2)Sb_6, both Ca_(5)Ga_(2)Sb_6 and Ca_(5)In_(2)Sb_6 have reduced phonon velocities and improved carrier mobility, suggesting that improved zT can be achieved in these materials. Here we further investigate Ca_(5)Ga_(2)Sb_6, which is an intrinsic semiconductor with a small concentration of p-type carriers. By substituting Zn^2+ on the Ga^3+ site, we show that it is possible to increase and control the carrier concentration in Ca_(5)Ga_(2−x)Zn_(x)Sb_6 and thus optimize its thermoelectric behavior. A single parabolic band model was used to estimate an effective mass of m* = 1.6me, which is slightly lower than Al-based compounds. Though the reduced m* leads to a lower Seebeck coefficient, it also leads to a much higher electronic mobility. The high mobility leads to increased thermoelectric figure of merit (zT) at low and intermediate temperatures relative to Zn-doped Ca5Al2Sb6. However, due to the decreased band gap in Ca_(5)Ga_(2)Sb_6 relative to Ca5Al2Sb6, the maximum zT in optimally doped Ca_(5)Ga_(2)Sb_6 is reduced (peak zT ~ 0.35 at T = 775 K)