Unfortunately, no, the 2005 Chevy Malibu does not have Bluetooth capabilities, as Chevrolet—or rather, General Motors—would not offer Bluetooth on any of their vehicles until 2009, despite the technology being available as early as 2001.
This does not mean you’re entirely out of luck, as several aftermarket head units/FM transmitters are compatible with the 2005 Chevy Malibu—so if having Bluetooth is important to you, take a look at what companies such as Sony, Alpine, Kenwood, Bose, or JVC have to offer.