The rated power of a 2 kW generator is 2 kW, and the maximum power can generally reach 2.2 kW. In other words, a 2 kW generator can meet the power requirements of electrical equipment rated at 2 kW. In simple terms, it can produce 2 kilowatt hours of electricity per hour.
The family you mentioned uses 5 kilowatt hours of electricity every day, so the situation is complicated. If this family only uses electricity 2 hours a day, then a 2 kW generator is not enough for a family. The number of households that can use a 2 kW generator depends on the power of the electrical appliances used by each household at the same time, provided that the power of the electrical appliances used by each household at the same time does not exceed 2 kW. A 2kw generator can provide up to 48 kilowatt hours of electricity, which can theoretically be used by 9 families, at condition that each family uses it at staggered times (it's a bit difficult). You can calculate the total power of each household when electrical appliances are used the most at the same time. As long as the total power is not more than 2 kW, the usage requirements can be met.