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ADS 11060 C is a double lined spectroscopic binary with a period of 25.7631 days and an eccentricity of 0.565. Spectral types of the two stars are estimated as K7 V and MO V with a magnitude difference of about 0.55 mag in V. The stars appear to be somewhat metal rich with respect to the Sun. Despite the relatively large masses of 0.53 and 0.51 solar mass, our photometric observations find no evidence for eclipses and we estimate an inclination of 77 deg plus or minus 11 deg. ADS 11060 C is, however, photometrically variable with a period of 9 plus or minus 1 day and an amplitude of 0.05 mag in V. Thus, it is a newly identified BY Draconis variable. The center-of-mass velocity of ADS 11060 C and an estimated parallax of 0.030 sec support its physical association with ADS 11060 AB, making this a quintuple system. The projected separation of the AB-C system is nearly 1200 AU. Although the log lithium abundances of the two components of ADS 11060 C are only upper limits, less than or equal to -0.14, lithium abundances of the AB-C components appear to be consistent with those of similar stars in the alpha Persei and Pleiades clusters, suggesting an age of about 70 Myr for ADS 11060 AB-C. The system is a possible member of the Pleiades moving group. Listed as an optical counterpart to a source in the ROSAT Wide Field Camera extreme-ultraviolet bright source catalog, both ADS 11060 AB and C may contribute to the observed flux.