Is the bolt pattern the same for a 2005 Toyota matrix and a 2010 cobalt?

No, the bolt pattern for a 2005 Toyota Matrix is different from that of a 2010 Chevrolet Cobalt. The Matrix typically has a 5x100 bolt pattern, while the Cobalt uses a 5x110 pattern. Therefore, wheels from one vehicle will not be compatible with the other without adapters.