Why a 5kVA inverter often trips on an air conditioner or pumping machine, and what size you really need.
It's the start-up surge
Motors — in ACs, fridges, freezers and pumping machines — pull 3–5 times their running power for a second when they start. A 1HP pump that runs at 750W can demand over 2,000W at start-up. If the inverter can't supply that surge, it trips.
What size you need
One inverter AC (1–1.5HP) with the rest of a flat: about a 6kVA inverter, 10kWh+ of lithium and 3.5–5kW of panels.
A pumping machine on its own is fine on a 3kVA+ inverter if nothing else heavy starts at the same time. Run it in the afternoon when the sun is charging the battery.
Regular (non-inverter) ACs are much harder on solar. If you're buying a new AC, get an inverter model.