You want a 1 channel, 5V relay module, not just a relay. If you search Amazon for “5V relay module,” you will find many listings. It is likely the current limit on a 5V digital pin on the Rambo board is 40ma. Relay coils usually draw more than 40ma, but a relay module will only draw about 5ma of trigger current.
There are some 12V pins on the board that in theory you could use instead of a relay. The fan pins are enabled, and they could be used without modifying the firmware by using M106/M107 to control the pins. Or you could reassign them to M7/M8 in the firmware. I use fan pins to control the power to my router, and also to my air assist for my laser using an IOT relay. The problem is that, according to your picture, you need 6.5W, and I don’t know if fan pins are rated for 6.5W. There are heater pins for the extruder and for bed that will definitely handle the current, but V1 instructions don’t have power wired to these pins, plus I don’t know if the V1 maintained firmware has the heaters enabled in the firmware even if you supplied the power for the heaters.
Edit: I took a look at the schematic for the Rambo board. According to the schematic, Fan 2 use a NCV8402AD MOSFET. According to the datasheet it should handle around 2A, so the 0.55A for your use, should be okay…at least as far as the MOSFET controlling the pins is concerned. I picked Fan 2 because I know it has power since I use it for my IOT relay so know it is powered.
Edit 2: Fan 0 and Fan 1 use a PSMN1R8-40YLC MOSFET, which according to the datasheet will handle 100A. It appears that the only pins not powered by V1’s instructions are the heated bed pins. The pins for extruder heat are powered and use this same MOSFET.