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.

This is wrong advice.

The relay's datasheet will tell you any limitations in the relay's duty cycle (on-time to off-time). In general the coil's voltage rating is continuous.

A series resistor could be used to run a 5 V relay from a higher voltage supply. If series resistance is added when the supply voltage and rated voltage are the same then the pick-up speed will be extended and arcing at the contacts may occur due to slow switching speed.

From the comments:

What is pick-up speed?

Releys are mechanical. When the coil is powered the armature gets pulled in against the force of the spring and the contacts close - usually with some wiping action to clean the contacts. Using a lower-than-rated voltage for the coil will cause the relay to pull-in / pick-up more slowly than it would at the rated voltage since the magnetic force will be weaker.

So, 140 mW for power coil means I can dissipated that power continuously?

That is what the rating means.

Current for 178 ohm at 5 VDC is 0.028A. So, It can consume 0.028 A continuously.

Correct.

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.

This is wrong advice.

The relay's datasheet will tell you any limitations in the relay's duty cycle (on-time to off-time). In general the coil's voltage rating is continuous.

A series resistor could be used to run a 5 V relay from a higher voltage supply. If series resistance is added when the supply voltage and rated voltage are the same then the pick-up speed will be extended and arcing at the contacts may occur due to slow switching speed.

From the comments:

What is pick-up speed?

Relays are mechanical. When the coil is powered the armature gets pulled in against the force of the spring and the contacts close - usually with some wiping action to clean the contacts. Using a lower-than-rated voltage for the coil will cause the relay to pull-in / pick-up more slowly than it would at the rated voltage since the magnetic force will be weaker.

So, 140 mW for power coil means I can dissipated that power continuously?

That is what the rating means.

Current for 178 ohm at 5 VDC is 0.028A. So, It can consume 0.028 A continuously.

Correct.

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.

This is wrong advice.

The relay's datasheet will tell you any limitations in the relay's duty cycle (on-time to off-time). In general the coil's voltage rating is continuous.

A series resistor could be used to run a 5 V relay from a higher voltage supply. If series resistance is added when the supply voltage and rated voltage are the same then the pick-up speed will be extended and arcing at the contacts may occur due to slow switching speed.

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.

This is wrong advice.

The relay's datasheet will tell you any limitations in the relay's duty cycle (on-time to off-time). In general the coil's voltage rating is continuous.

A series resistor could be used to run a 5 V relay from a higher voltage supply. If series resistance is added when the supply voltage and rated voltage are the same then the pick-up speed will be extended and arcing at the contacts may occur due to slow switching speed.

From the comments:

What is pick-up speed?

Releys are mechanical. When the coil is powered the armature gets pulled in against the force of the spring and the contacts close - usually with some wiping action to clean the contacts. Using a lower-than-rated voltage for the coil will cause the relay to pull-in / pick-up more slowly than it would at the rated voltage since the magnetic force will be weaker.

So, 140 mW for power coil means I can dissipated that power continuously?

That is what the rating means.

Current for 178 ohm at 5 VDC is 0.028A. So, It can consume 0.028 A continuously.

Correct.