Maximum discharge current of battery cabinet

What is a good battery capacity?

If it lists the capacity as 50Ah at C/20 (common for lead-acid), that's 2.5A so you might want a better battery. EDT as Andy says, if your device draws bursts of higher current, you also need to know the max (not continuous, maybe called peak) discharge current of your battery matches whatever your load needs.

How do you know if a battery has a Max discharge current?

There is no generic answer to this. You read the battery datasheet. Either it will tell you the max discharge current, or it will tell you the capacity at a particular discharge rate, probably in the form C/20 where C means the capacity. You know the current you need : 4.61A.

What is the maximum discharge rate of a 5AH NMC cell?

These numbers are quite typical of a 5Ah NMC cell. Peak discharge is around 10C. However, there are other factors that determine the maximum discharge rate. The cell will be designed to deliver a maximum current versus time. This will be dependent on: Comparing power versus energy cells we see there are some fundamental differences.

How do I know if a cell has a maximum discharge rate?

First of all though we need to look at the cell specification sheet as this really should define the maximum discharge C-rate or current along with the minimum cell voltage. It will also give a temperature range over which the cell is able to deliver that discharge rate.