Resistor ratings for inductor fly-back suppression
You are getting muddled.

It's not the 5 volts that is used to power the relay that needs to be factored in when designing a resistive flyback suppressor, it's the maximum voltage that your driving circuit can withstand under flyback conditions that has to be considered.

For instance, consider the situation of using an NPN (or N channel) transistor to activate a relay. When the relay is deactivated, the inductive 250 mA would produce a peak voltage of 25 volts in a 100 ohm flyback resistor. This means the collector (or drain) of the transistor would see a peak voltage of 25 volts plus 5 volts (30 volts).

Therefore, if the transistor has a voltage rating greater than 40 volts (a little added margin) then you would be good to go.

Regarding the power rating you don't need to pick a resistor that has a rating equivalent to the instantaneous value of the power surge; resistors are usually very good at handling largish short power surges so, if the flyback surge is done in less than 10 ms (fairly normal) then pretty much any quarter or half watt resistor will do the job.