So I have a small problem with my Arduino Pro Mini here. May be worth noting that it is a clone, but otherwise this is still some weird functionality. I have done some experimenting so I'll just set the scene for you. I have everything that requires power connected to the + and - lines on my breadboard, that way I can avoid drawing more than about 20mA across any individual pins. I currently have my Arduino Pro Mini hooked up to the 5V power supply via the RAW and GND pins, but the supply is a regulated 5v wall supply. It actually is currently outputting 5.36V.
I have made sure all my pins I'm using for output are indeed set as output, the problem only arises when I attempt to power the device from something OTHER than USB power. I tested the output from my wall adapter connected to RAW and to a random VCC pin, both have the same effect.
When powering the device via USB (USB to Deek-Robot ASP, then to Pro Mini), if I set my digital output pin to HIGH, I get 5v. This is enough to turn on a 5v relay that then supplies power from the supply to a small water pump. However, if I use the regulated wall-power, I get about 3.7 to MAYBE 4.15v, which sadly is not enough to switch the relay to the NO position.
I have tested the voltage coming from the USB ASP as well, it is 4.95v.
EDIT: The wall-plug voltage drops from 5.36 with no load except the meter to 4.7v with the Arduino and a couple LEDs attached, if that means anything.