Relays need a certain amount of power to operate. For a given size you can often reduce the current needed if you can select a higher supply voltage with a matching voltage relay. A 12V relay could easily consume 5/12 of the current of your current 5V relay.
The resistor in parallel with the diode and coil does not serve much purpose. As a snubber the value is too large and as a pull-up it is not needed. The relay coil already provides a DC path for any currents that are expected.
The 1N4149 diode is a small signal switching diode and the snubber diodes are often selected from the more robust rectifier type diodes if there is any doubt that the fly-back currents could exceed the current handling of the lighter duty signal diode.