filament led bulb inrush current
Look at the listed amp rating of your bulb

You need to look at your bulb's documentation/data sheet for its listed draw in amps.  If it provides a VA rating, you can compute amps from VA/volts.  If it provides actual watts and power factor, you can compute Watts/Volts/PF.  LED bulbs are often marketed as "Same brightness as a 60 watt incandescent bulb", that is a meaningless number. 

Look at the rating of your relay

Inrush current is a big current surge on initial startup, but no particular reactivity when interrupted.  (contrast with an inductive load which has a huge kick when interrupted, and the kick can leap across contacts).  The inrush current on your consumer LED-based lamp product is lesser than that on an incandescent bulb.  Look at the rating on the relay.  Relays are listed at different power ratings for


resistive (usually the highest number)
motor (huge inductive kick)
ballast (meaning magnetic ballasts, also a big inductive kick)
Tungsten (meaning incandescent bulb, meaning inrush current) 


If it lists a tungsten amp rating, then you can use that figure straight-up; they already compensated for inrush current and UL/CSA/TUV etc. listed it as such.  You don't need to.    

Comply with Code - use the right relays

Since you are switching mains voltage, you must also comply with your local electrical codes.  They will require that you use not random components, but assemblies listed for mains use.  Contrast: 




The first is a bare component, you'd need to solder wires to it and then what?  Wrap it in electrical tape and leave it to flop around in a junction box?  Unacceptable with mains. 

The second one is designed to mount on a standard junction box fitting. Note how this puts the mains wiring inside the junction box, and the low-voltage wiring outside. This satisfies separation requirements of high voltage and low voltage wiring.  Once outside the high-voltage "envelope" you are subject to the much more liberal low-voltage wiring rules, same as telephone; or doorbell or thermostat in countries where that is low-voltage. 

Relay the relays

There are many relays like the second one.  Some may be 5V coil. But other voltages will be much more readily available, e.g. 24V is popular in North America. This may not be a problem: some have a built-in transformer that matches their coil.  These devices supply you 2 wires - if you short them, the relay picks up.  Simple as that.  You can do  that with the 5V relay of your choice. 

Even better, 24V travels well.  That means you can switch the mains voltage in the location that makes sense, i.e. down at the service panel/mains supply or somewhere it's easy to access an electrical box to mount it... keep the 5V near your PC... and let the intermediate coil voltage do the traveling.