thinking again I seem to remember the HC-05 uses 3.3V logic, e.g. my HC-05 has "LEVEL 3.3V" against RX and TX pins
the Nano uses 5V logic therefore use a level converter or potential divider between the Nano Tx and HC-05 Rx or you could damage the HC-05 - see Interfacing-HC-05-Bluetooth-Module-With-Arduino
one reason why I tested the HC-05 use an Arduino Due and a ESP82666 both of which use 3.3V logic