ADC readings after waking up from POWER-DOWN

Thanks for the suggestion. I have adjusted the loop like so:

void loop() {
int value = analogRead(A0);
value = analogRead(A0);
Serial.print("First value: ");
Serial.println(value);
sleeping();
int new_value = analogRead(A0);
new_value = analogRead(A0);
Serial.print("Second: Value");
Serial.println(new_value); 
}

This is the output on the serial monitor:

��Z�.␗���Օ� 518
Second:␀���Օ�18
First value: 521
Second:␀���Օ�15

Interestingly, if I pot both analogReads into separate for-loops of length 5 e.g., most of the readings are sensible. Perhaps there is some setup time that I'm unaware of?

Edit:
In an earlier version of the same project, I simply added some delay(10) before each ADC reading which also gave me reasonable readings.