Many factors determine system production. Your solar professional may have provided a production estimate that was based on a solar energy estimation tool like PVWatts. Solar energy estimators use geographic region, seasonal variation, and other factors like roof pitch, wiring, and electrical losses to calculate production estimates.
For a simple estimate, use the following equation:
DC System Size x hours of sun/day x system efficiency = estimated AC daily production
5 kW x 5 hr/day x 0.77 = 19.25 kWh/day