Controlling Relay with FPGA
You are correct that you need 5 Volts for the relay however you are going also need to source ~30mA to turn on the coil.

Coil voltage: 5VDC 
Coil Resistance: 178 Ohms

V=I*R = I=V/R   5vdc/178ohms=0.028Amps

If you have a 5 volt power source you could use it to power the relay; and then control a transistor with your FPGA to open and close the low side of the relay circuit.