I know that I shouldn't use the Arduino to power there servos, I learn it the hard way.
So my robotic projects now always use exnternal battery for the servos. The triple is I ave to use tow battery which adds more weight and size. Would it be fine to use a 6V 5000mAH battery pack to power both? TIA
Being powered from the same battery should work OK, if you run separate runs from the power and ground of the battery terminals to the Arduino, and from the battery terminals to the other loads. The reason you want separate power runs is that there is an additional voltage drop from the wires. Of course, the 6V battery pack will likely drop to 4V as the battery gets depleted, so you might want a switching regulator to power the Arduino. Otherwise, that 4V on the Vin will become 3V on the 5V line, which isn't good.
The usual reason there is a problem when running an Arduino and servo(s) from the same source is that the servo's heavy load will drop the voltage. A nearby battery does not sag nearly as much as a 'wall wart' power supply on the end of a long cord. Also, a battery will absorb a fair amount of transient voltages that a servo might create. Electronics prefer a steady voltage so they act predictably.
You can run servos and the Arduino from the same power source providing you have enough decoupling on the supply.
The problem is that 6V is not high enough to run the Arduino external power connection (7V minimum) and 6V is too high for direct connection to "5V" on the arduino.
The best solution is to use a 9 to 12 volt battery and feed that to both the Arduino external power and to a switch-mode power supply that can provide separate 5V at the current you need.
The YourDuino RoboRED that I worked on developing has both a UNO compatible arduino compatible and a 5V 2A switching power supply on the same UNO-size board. Info HERE:
How much servo current do you need?
DISCLAIMER: Mentioned stuff from my own shop...