Why does my microcontroller's 5V out fail to activate my 5V relay?
The relay module in the photo has a driver transistor on board (as well as a couple indicator LEDs and a catch diode)-- the input impedance looks to be in the 2K ohm range, which is pretty low, but your micro should be able to supply it. 

You need to supply a solid 5V supply to the relay unit for it to be able to work. The input is just a control input. If you don't have a separate 5V supply, the on-board transistor will not be able to amplify the weak output of the micro- the relay takes far more current than the micro can supply. Make sure there is a solid common ground connection. This is very important. 

Check that the supply voltage is 5V (input on or off) and that the input voltage is at least 3V (on), and it should work.