Ok I started with 220Ω resistors. 3 is enough to keep it on, I counted more than 30s with all 3 of them on. What I have in my project, to the base of the transistor it a 1.1kΩ.
So, you need about 73mA, I would use a 56 Ohm 1 Watt (90mA) or 2 100 Ohm 1/2 Watt (100mA) resistors for dummy load.
Put your Nano on the breadboard and connect the dummy load and transistor like this with a 1k resistor from pin 8 to base.
Power the Nano from computer USB, not from powerpack yet, you will need a jumper from powerpack - to Nano GND.
Upload this test sketch to Nano and adjust interval time and pulse length to the minimum that will keep the powerpack alive, we start with a 5 second interval and 100 mS pulse length, start Serial monitor and set to 115200 baud, in the top of serial monitor type desired interval in seconds, for example, 10 seconds, type letter "i" then 10, like i10 then [ENTER], for pulse length of 75 mS, type p75[ENTER], increase interval time a few seconds at a time until the powerpack starts shutting down then back up a second or 2, decrease pulse length the same way but I would stay above 50. I found an interval of 12 seconds and pulse of 50mS works for one of mine.
unsigned long iStart; // interval start
unsigned long iEnd = 5000; // interval end
unsigned int pLen = 100; // pulse length
const byte pPin = 8, // pulse pin
ledPin = 13; // led pin
void setup()
{
Serial.begin(115200); //set serial monitor to match
pinMode(pPin,OUTPUT);
pinMode(ledPin,OUTPUT);
prntIt();
}
void loop()
{
digitalWrite(pPin,millis() - iStart < pLen);
digitalWrite(ledPin,digitalRead(pPin));
if(millis() - iStart > iEnd)
iStart += iEnd;
while (Serial.available() > 0) {
char inChar = Serial.read();
if(inChar == 'i')
iEnd = Serial.parseInt() * 1000;
else if(inChar == 'p')
pLen = Serial.parseInt();
else
{
Serial.println("invalid input");
while(Serial.available() > 0)
Serial.read();
}
prntIt();
}
}
void prntIt()
{
Serial.print("interval = ");
Serial.print(iEnd / 1000);
Serial.print(" pulse length = ");
Serial.print(pLen);
Serial.println("\n");
}
ok well im using pin 7 because 8 is busy.
Did you mean to post new code? Because I think you forgot to paste it in 
Here is a resistor I got (not currently in the circuit). According to color code it is 47Ω:
ps: when is this forum going to allow users to post an image/link from the start?
Did you mean to post new code? Because I think you forgot to paste it in
That was my fault (I'm old) 
47 is a little low, but it's only going to be on for a few mS at a time.
BTW, are you sure that powerpack can do 5 servos at the same time? What's it's mAh rating?
That's OK I'm probably older.
It's a 23,000mah pack.
OK I'll look or a bigger R. The 47 is running right now. So far so good but the led lasted about 12 hours so.
And yeah the 47R is getting a but warm
