americanaudiophile is right... 3.5mm mini jack cable on both side should work but i heard something from a consultant inside a shop specialised in audio. i'm not able to confirm but i heard it was better to use a RCA Audio cable (the old fashion left en right white/red connectors) on the output side (the TV) and then plugged on your 3.5 mini jack input on your 5.1 Sony.
i was in the same situation as you are, only i didn't have 5.1 but a 2.1 soundbar.
he told me that using the headphone output from the TV was not as good as the stereo audio output because something was already processed by the TV on the headphone output. not sure what he meant and if it's true... but i can imagine it's processed by the TV to deliver the sound on the headphone. anyway...based on what that guy told me... i would rather choose a RCA cable on one side and a 3.5 mini jack at the other side of your cable.
your post is from the beginning of july so i can imagine you already decided for a solution. please let us know what you did and if it works and how it sounds !
with that solution, you will sadly not get a surround effect but if it's for watching a normal chanel...i doubt they broadcast their audio in 5.1 anyway. if it's for watching movies on DVD or BR...that will be another story...you will miss the 5.1 output, unless there is a way to plug your DVD or BR player right away into your Sony