Generate 5VDC signal when external sensor input changes from high to low
This is literally the simplest Arduino program possible.  I can't believe you couldn't find an example of making one pin HIGH when another goes LOW.  

void setup(){
  pinMode(yourInputPin, INPUT_PULLUP);
  pinMode(yourOutputPin, OUTPUT);
}

void loop(){
  if(digitalRead(yourInputPin) == LOW){
     digitalWrite(youOutputPin, HIGH);
  }
  else {
     digitalWrite(yourOutputPin, LOW);
  }
}


All you need to do is supply the appropriate pin numbers.