Yeah check the wirering. Also, there are HC05 Modules out there that have 5V logic on the rx and tx lines (i know because i have one), so make sure yours is in fact 3.3V level. Otherwise loose the voltagedivider on the modules rx-pin. Also check the baud-rate. I think these things come with 9600-Baud, but that can be changed.
Also try not powering the arduino from USB if youre doing that. Could be that the usb-uart chip is interfering. Not sure about that though, i only ever used those modules with SoftSerial on Arduino.