Using 5V battery supply for UNO and servo?

I’ve compiled and tested a sketch whose main output is to activate a servo (HS-311). Now I want to run it from a single external supply (rather than the PC USB and a separate regulated 5V bench supply). It would be convenient if that single supply could be my 5V high capacity battery pack (that I sometimes use for re-charging my iPhone when away).

Is that a reasonable idea? And, if so, should I connect it to the UNO’s 5V pin please, as well as direct to the servo supply?

That sounds perfectly fine. You can connect the 5V+ directly to the + of the servo and either the 5V or the RAW pin on the Uno. If connecting to the RAW pin, the built in voltage regulator on the UNO may lower the supply voltage to the Atmega a little bit, but usually that's no problem at all.

The only situation, where I had to add a capacitor was with some digital servo's that caused power fluctuations. Your HS-311 is an analog servo, so usually not as power hungry as the digital ones.

Using the RAW has no advantage at all, only creates problems.

hmeijdam:
If connecting to the RAW pin, the built in voltage regulator on the UNO may lower the supply voltage to the Atmega a little bit, but usually that’s no problem at all.

Using the “VIN” pin with a 5 V supply is a very bad idea, will lower the operating voltage substantially, will not be regulated and is very likely to cause problems.