Most likely this is due to lack of understanding.

I am hoping to drive a pump that is used to operating with a power supply that can go from 3V to 12V. DC 3V~12V-5A. I will be using ideally an Arduino Nano but if I must use an UNO I will.

I am a bit confused because most of the relays I can find output 10A or 12A or more. Cant find one that outputs 5A.

I dont know enough about the pump to know how catastrophic it would be to provide it with more than 5A but a 5A power supply is what came with it.

Where might I be able to find a relay that can be controlled from a Arduino (ideally Arduino Nano) and output anywhere from 3V to 12V at 5A? Bonus points if it can do a few levels in-between 3 and 12V but normally I keep the power supply at about 8V.

Edit: Thanks all! From reading your responses (and some from other threads) the plan is:

Arduino Nano iOT powered by USB with those connections soldiered so the Arduino Nano outputs 5V

Then Channel Relay Module Board Shields 5v Relay Modules Channel Relay Boards with Optocoupler Isolation High Low Level Trigger 

Going to use a 4FT DC 5.5MM x 2.5MM Female Plug to Bare Wire from my old power supply to the relay

And then a DC 5.5MM x 2.5MM Male Plug to Bare Wire to the pump.

Will 3D print my enclosure once everything is soldiered and tested and insulated. Going to also be using a Water Sensor Detector that runs on 3.3-5V DC and a two pin Micro Momentary Tact Switch.

Prototyping on an Arduino Uno R4 with breadboard, a multimeter, and some breadboard pins.

Should be fun and I have a lot to learn. Specifically going to be fun to understand the parts of this where the relay has to handle the inductive load of the pumps motor.