The radio emission from the well-studied massive stellar system Cyg OB2 #5 is known to fluctuate with a period of 6.7 years between a low-flux state when the emission is entirely of free-free origin, and a high-flux state when an additional non-thermal component (of hitherto unknown nature) appears. In this paper, we demonstrate that the radio flux of that non-thermal component is steady on timescales of hours, and that its morphology is arc-like. This shows that the non-thermal emission results from the collision between the strong wind driven by the known contact binary in the system, and that of an unseen companion on a somewhat eccentric orbit with a 6.7-yr period and a 5 to 10 mas semi-major axis. Together with the previously reported wind-collision region located about 0.8 arcsec to the north-east of the contact binary, Cyg OB2 #5 appears to be the only multiple system known so far to harbor two radio-imaged wind-collision regions.