The 5V @2A you have should work. I currently can't see attachments so I could not see your picture. I'm wondering if you had the power adapter correctly wired to the relay board?

The +5V from the power adapter goes to the Vcc pin of the relay board.
The ground from the power adapter goes to the relay board GND and to the Arduino board GND.
The Arduino outputs go to relay board IN1, IN2, etc.