MacTracker does not list an iMac 5,2 but according to them the iMac 5,1 (late 2006) does have builtin bluetooth 2.0 + EDR. As V1 said, it may be the bluetooth module has failed. If the model number is correct, it is officially obsolete, so it will not be supported by Apple or the Genius Desk. You will need to find a third party and parts will be difficult to come by.
"All you've got to do is own up to your ignorance honestly, and you'll find people who are eager to fill your head with information" --Walt Disney
