Can onstar work in your 2005 Chevrolet Cobalt?

Yes, OnStar was available as an option in many 2005 Chevrolet Cobalts, but it's important to note that the OnStar service itself is no longer active. General Motors discontinued service for most vehicles that old. Even if your Cobalt had OnStar installed when it was new, the hardware may still be present, but the cellular connection and service subscription would be long expired. You cannot reactivate it.