A 9V alkaline battery voltage quickly drops to 7V then drops slower as it is used. But an ordinary 7805 regulator stops regulating when its input is 7V and less.
Use a "low-dropout" 5V regulator instead that works perfectly when its input drops to 5.5V or less.
The datasheet shows the current that is used by the regulator. Some regulators use a very low current.
A resistor in series is not wanted.
A voltage divider has NO voltage regulation. The output voltage varies when the input voltage varies and the load current varies.