You microphone input is connected to the +5V line and the preamp used 0V as the signal ground - that's likely to cause over-sensitivity to the power rail noise I think.
The standard electret connection is for the load resistor to be on the high-side of the electret, and for it to be split in half and decoupled in the middle - thus all the low-voltage signals are referenced to GND. Another way to decouple the electret would be to add a resistor between it and the 5V rail and decouple the +ve side of the electret - minimal change to current circuit.
If the electret acted as a perfect current source your circuit would be fine, but I suspect its not a perfect current source so you get line noise at the input of the LM386.
The line noise is caused by the digital electronics, in general using a separate voltage regulator for the analog electronics is a good precaution when handling low-level signals. The voltage regulator on the existing 5V rail has to fight the digital noise and basically it won't eliminate it, just reduce it. A separate regulator is free from such problems.