Electronic – NE5532 slew rate

That particular op-amp is capable of hundreds of mA output current. I think you should be able to deafen yourself if the headphones are the normal rare-earth ~30\$\Omega\$ variety.

You seem to have identified part of the problem- the supply voltage drops. You need to capacitively couple the headphones. What you have now attempts to put 2.5VDC across the headphones, which is at least 83mA, thereby dragging down your supply.

Try a 100uF electrolytic in series with the output (+ side to the op-amp, - to the headphones).

You would change the current in order to modify the tradeoff between performance (higher currents mean higher slew rates on internal nodes) and power consumption. That allows this single design to address a wider range of applications.

The odd symbol just seems to be another name for the negative supply (pin 4), which is where the other end of the resistor needs to go.