How to generate a -5V to +5V sine wave from one DC supply?
This design should help you a good way on towards your aim although it won't provide the full +&amp;- 5V, maybe +&amp; -4V. I chose the common op amp for its rail to rail output capability and low input bias currents.

It's a Wien Oscillator followed by a variable gain power stage.

R6 &amp; R7 linearise the J-Fet.



EDIT

This bootstrapping technique should get you up to +&amp;- 5V. I've split the output transistors' base resistors and added the capacitors.