At 5v the 180 ohm resistor should provide 27ma to the TLP521. The TLP521 has a Current Transfer Ratio of 50%, which should provide 13+ma to the relay coil which requires 12ma to operate.
Sorry...I neglected to state that I also feed +5v and GND to the coil side of the optocoupler. The +5v is coming straight from the power supply. The power supply is rated at 500ma and my entire circuit is currently consuming ~30ma, so the additional 40ma shouldn't be a problem at all for the power supply.-Mitch
You have wired the output transistor wrong, it needs to be in a 'low side' npn switching configuration. Ground the emitter pin 9, wire pin 10 to C1 on the relay, wire C2 on relay to +5vdc. That should work.