Solar requirements for 5000W equivalent system
I currently run a fridge-freezer and larger freezer, some lights and computers off of a 5000W, 220V to 110V (50 Hz) transformer.

It sounds as though a 1 kW system should be adequate.

Q1. Would a 5000W (pure sine wave) inverter be able to run the same loads as the 5000W transformer?

Yes.

Q2. What size battery bank how many (Ah) on a 24v setup would be needed?

You haven't specified the required run time from the batteries.

Work out the energy storage your load requires in watt-hours (Wh) for the required run time.
Since power = voltage × current (P = VI) and energy, E = P × t you can work out the ideal battery capacity from \$ Ah = \frac E V \frac 1 {Eff} \$ where Eff is the efficiency of your inverter.


... (assuming constant charge from solar &amp; Wind sources).

This makes it sound as though you don't require any storage.