My buddy got me a JBL SCS500.5 surround sound system. It uses a purple LFE cable to connect to the tv. I have a Panasonic P50ST30 that has a digital audio out port on the back (optical). I have zero experience with connecting this stuff but I assume I am going to need an adapter or converter of some sort?
There is no way to connect the two. A sub can't accept a digital input. You need a receiver to power the speakers and the sub connects to the receiver. Your sources (ie cable box/Satellite box, DVD/Blu-Ray, gaming consoles, etc.) connect to the receiver and then the receiver connects to the TV. The receiver is the main hub for a surround system, everything connects to it with various type of connections.
As eljaycanuck said, your system is not complete. You need to get a receiver to power the speakers and to interface between the TV and the speakers. There are quite a few low-cost 5.1 receivers that will work well with the speakers.