what is the use of a capacitor and a resistor in series and a diode in between them with diode's positive connected to ground?

in the circuit attached it is before the amplifier section with pn2222a

 

C5 and R5 form a differentiation circuit that turns the positive going square wave edges into short pulses that turn on the flyback transistor for short periods of time. D1 provides a discharge path for C5 when the square wave goes negative.

 

The reason for restricting the excursion of the negative-going spike at the base of the transistor as noted by jimkeith is that if the amplitude of the negative-going spike is significant, it can damage the transistor. So the diode is there as a protective measure against damage to the transistor's base-emitter junction.

hgmjr