That combination is actually a solid entry-to-mid-range package, provided the battery voltage matches the inverter.
If you’re using:
• Anern 4.2 kVA inverter (24 V model)
• Africell 5 kWh LiFePO4 battery (24 V)
This setup can comfortably power:
• TVs
• Fans
• Lights
• Refrigerators
• Routers
• Laptops/desktops
• Small pumping machines
• Washing machines (one at a time)
• Microwave ovens (briefly)
You should avoid running multiple heavy appliances simultaneously, such as an electric kettle, pressing iron, water heater, or large air conditioner, because together they can exceed the 4.2 kW inverter rating.