I have been told that always that I add a relay to my design I have to include a series resistor (series with the coil) to limit current in it. So, I want to use a 5VDC (Coil) relay. How do I calculate that resistor? In the relay's datasheet I can read my coil has a resistance of 178 ohm.

The power of the relay is 140mW. Actually, if you calculate the power with 5VDC and 178 ohms the result is 140mW (I * I * R = 140 mW). So, I guess the series resistor is to avoid that the coil is always at maximum capability, I mean, to have a safety margin for the component, isnt it?

Is that the purpose?

If it is, I see a problem, the voltage drop in the series resistor will cause that the coild would not be at 5VDC and maybe the resistance change too.

If not, could I connect the terminals of the coil directly to Vcc and Gnd? Or maybe that value os 140mW is not the coil power (?)