How much current does an Arduino Mega draw from a LiPo battery (5,000 mAh)?
The important thing to realize here is that the capacity of the battery does not affect the amount of current drawn. Your Mega will draw the same whether it is connected to a 1000 mAh battery or a 5000 mAh battery. The larger battery will just last longer.

Tests on my Mega2560 Arduino show that (with no peripherals connected) it draws about 70 mA from a 7V supply, and slightly more (72 mA) from a 12V supply (the voltage regulator has to throw away some of the extra voltage as heat). (However, see below)

The exact amount it would draw in practice would be strongly correlated to what things you have connected. For example, LEDs, motors, shields, other devices.

I have a page about power saving that you might find useful if your objective is to minimize power usage.



Edited to add more about power consumption

It appears that my initial claim that the current consumption goes up with an increase in voltage was wrong. With Majenko's help I made up a detailed set of automated tests, increasing the Mega2560 power input by increments of 200 mV, taking a reading from both the power supply and my multimeter, averaging each one over ten readings, and plotting the results. This is what I got:



The two measurements seem to be consistently different by 0.2 mA. What this shows is that at 7V, the current consumption is 65.3 mA, and at 12 it is 64.1 mA, about a milliamp less.

I do, however, stick by my original assertion that the capacity of the battery will not affect consumption, and a larger battery will just last longer.