The wiring diagramme is junk, and it is likely that any other information from the same source is too. I'm surprised that you could upload the code. The communication lines are in the wrong place and the wrong way round. Further, it is good practice to have a voltage divider in the Arduino Tx line but, if you haven't done that, don't panic, it probably isn't fatal.
Since you appear to want Arduino<>Arduino comms, check here
http://www.martyncurrey.com/arduino-to-arduino-by-bluetooth/#more-2922
for somebody who really knows what he is doing.
If you have the on-board LED flashing slowly, 1flash/2sec, it is indeed in AT mode, but that merely means the power connections are OK. (This is actually a good start) Pretty well all HC-05s that are on a breakout board as you show run on 5v power, and most are marked accordingly on the back of same.