Don't forget that the flyback diode is absolutely required - otherwise the relay coil inductance can easily destroy the transistor, and possibly other parts of the circuit.
I'd suggest not using a darlington for low voltage switching like this - a darlington costs at least a volt, sometimes 2V, so your 5V supply is only 3V at the relay winding. Or use a 6V supply, darlington and 5V relay... Darlington's tend to run hot because of the wasted power too.
A single switching transistor, if saturated, only costs 0.05 to 0.2V lost, shouldn't get very warm. Make sure it has plenty of current overhead (so for a 200mA load use at least a 500mA transistor, otherwise its hard to get good saturation).