Battery bank & Inverter compatability ?

The 420 ah capacity is only if you draw the power down over 20 hours... In other words, your battery bank has a 420 ah capacity only if you draw 21 amps (420 amphours ÷ 20 hours = 21 amps). 

You can safely draw more than 21 amps, but due to Peukert factor your capacity will be less than 420 ah.

Your 4000 watt load for 5 minutes does represent 333 watthours of energy, but your battery bank is much less than 20,160 watthours when you draw over 90 amps from the battery.

--vtMaps

The 20 hour C rate is the best case scenario. If you use a more realistic discharge rate, say 5 times that overly slow rate you can expect to about 15% less amp hours.

I am going to estimate the 20 hour C rate for that bank is around 20 amps. If you were to use say 5 times that power or 100 amps it would drop your amp hours to about 370.

83 amps should be fine.

These are good questions. The easy rules for FLA is 0.25C peak discharge rate, and 0.1C peak charge rate.

I'm running a magnum 4448 inverter with a 420ah battery bank. If my load is 4000 watts for 5 minutes, that would be 333 watthours of energy

So peak discharge amps is: 4000W/48V/0.9 (eff)= 92.6A DC.
For 420Ah thats a discharge rate of 92.6A/420Ah= 0.22C. That is within (at the top of) the recomended discharge rate for FLA. (100Ah per kW of inverter).
And, running your inverter at high power like that will (ignoring peukart, and exact voltage) flatten your battery to 0%SOC ie DEAD flat in: 420Ah/92.6A= 4.6 hours. Or to the recommeded 25% daily DOD, in = 420Ah/92.6A*0.25= 1.1hr

So, as Dave said, not something you want to do much after dark at any time of the year.

 The battery would have to supply 4000 watts ÷ 48 volts = 83.3 amps. Maybe another 8 amps or so for inverter inefficiency and I'm drawing over 90 amps from the battery. Seems harsh for long term battery life.
So in reality, the only time that I can use my inverter to it's capacity without battery damage is during full sun?

So interestingly, when you design a system to have a peak FLA charge rate of 0.1C you get peak charge amps as:
420Ah*0.1C= 42A
Solar needed to generate this is: 48V*42A/0.77=  2620Wp. Which, (quandaryily) is not enough to power the inverter at max load on its own. (But using AGM or LFP, you could get 48V*(420Ah*0.2C)/0.77= 5240W. Better huh?)

 If this is correct, whats a safe "max load" for this battery bank without incoming panel wattage?
Also what size battery is needed to maximize this inverter at night?

Its all a balance of elements. From the above you can see that to increase after dark Amps, or Watt hour requirements you need to increase the size of... everything.

Arkansasoffgrid said:

...and have never been below 84% batt after 3 overcast days....

That might be doing more damage to the batteries than a bit of heavy use. Batteries need to be used, I think your Midnite CC can even skip charging some days to allow your battery bank to cycle.