5v motor activated by IR remote control (HELP for scientific project on bird's conservation)

You are leaving out a lot of information still.
How often will the pump be operated?
How long will the installation be in place?
Where is the link to the data sheet of the pump.

Galapagos has a high solar intensity, so maybe a solar panel is worth a try, even under the canopy.

A note on your original setup,
rather pointless if you use the relay of the ready-made module, but maybe interesting:

I don't think that would be a good choice for an efficiency oriented setup.
I would use a simple low-side N-FET to switch the pump, if it were to be controlled by an Arduino.