Pre-Amplifying Electret Microphone for ADC Input
There are a few things wrong with your circuit. 

First, you need an op-amp that will function on 5V. Half of an LM358 might work for you. 

Second, you should divide the output voltage of the op-amp, not the power supply. 

Third, you must bias the op-amp so that the DC value of the output is near the middle of your ADC range. 

Fourth, your gain of 1,001 may be too large, and is certainly too large for a DC gain, you need to separate AC and DC feedback so that the DC gain is much less (close to one is good). Putting a capacitor in series with R2 would allow the DC gain to be 1. 

Fifth, whatever op-amp you use, you must have a DC path from both inputs to a bias voltage. Connecting the non-inverting input to the capacitor means it will float to some undesirable voltage in milliseconds. A resistor to an appropriate bias voltage will do.