relay driver (latching)
If you can use a 2 pole relay you can simplify the circuit quite a bit.
Connect your output to the base of an NPN transistor through a resistor as in your circuit. Connect the emitter to ground and the collector to the one side of the coil. Connect the other side of the coil to 5V. Connect the common of the second set of contacts to ground. Connect the normally open contact of the second set of contacts to the collector of the transistor. When the relay is energised, the contacts close and the relay latches itsef on, irrespective of future states of the transistor. The current used to drive the base should be 10 times greater than the collector current divided by the forward current gain to guarantee that the transistor is saturated.
B.Ib=10 Ic
The current is determined by the base resistor: Ib=(3.3-0.6)/R, assuming that the micro does guarantee 3.3 Volts output. Your micro must be capable of supplying this current.
If you need to be able to reset the relay, you will need a switch like a transistor to open the circuit to the coil. You could switch the 5V to the coil through a PNP transistor, or the ground connection to the contact common using an NPN.