Hmm are you talking about Logitech Z5500? As i don;t have both of them, and assuming that your 360 is having 2 "RCA" (not VGA) audio cables coloured white and red, you can just connect it via :
2 Stereo RCA (female) to 3.5mm stereo (female). But if you want to have 5.1 channel configuration of it, well i can't give the answer as i nvr see the back panel of both z5500 and 360
But remember for digital input, ask another techspot members as i'm really blind about co-axial or digital input