Help me understand stuff please.
If I wanted to charge a 56v 5ah battery from a 12v battery with an inverter 5 times, how big would my 12v battery need to be?
I understand that their will be energy losses at the transformer and the charger but how much ish? You also need lots of spare capacity in the 12v battery so you don’t deep discharge.
Anyone experienced at these things please?

DO you mean with a 240V charger plugged into a 12V dc to 240v ac inverter.
Whats the power rating of the charger?

56v x 5ahr = 280whr x 5 recharges = 1400whr
1400 / 12v = 116.666ahr for your 12v battery.

multiply by 2 to avoid discharging below 50% and then add a bit more for losses, call it 250ahr.

56*5= 280 Wh

280Wh / 12V = 23.3 Ah

x 5 = 117Ah

But the inverter and charger will not be very efficient. I’d probably double that at least to allow for that. [edit crossed post, I agree with the above, although I’d double again to be sure, some chargers seem to give out more in heat than they do electricity, not usually a problem with a cheap and plentiful mains supply].

Could you run whatever is 56V off a DC-DC power supply? I’ve got a 12V-24V power supply in my car, partially to get more oooph from the stereo, partially because it also isolates the stereo from the noisy power from the alternator. 12-56 is available just depends what current you need as to how cost effective it is.

Are you proposing to go from a 12V DC car battery to 230V AC then back down to DC changing voltages?
There must surely be a better way of doing that.

Sorry for the delay.
Yeah I should have said the inverter was 12v to 240v to use a standard charger. I think I read that the fast charger draws something like 10 amps but I can’t find it now. It does seem a little ridiculous but I haven’t seen a 12v charger for the batteries (ego garden power tools)