iPhone5 not showing up in devices tab on iMac, can't transfer songs from computer to phone

I have a new iPhone5 and an iMac running Snow Leopard.  I have scads of songs on my computer that are mostly from CDs.  When I hooked the new phone up to the computer, the newly purchased songs on the phone loaded onto the computer automatically.  However, the phone does not show up in the "devices" tab on the Finder and I can't see any way to transfer all the songs from the computer to the phone.  Many thanks for all help.  -J

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