The charging requirements for a Lipo battery are pretty simple:-
Current must be limited to the maximum rate specified for that battery, usually ~1C which is the same as the battery's capacity (390mA in your case).
Voltage must be limited to a maximum of 4.2V per cell, by reducing the charging current when the voltage reaches 4.2V.
You don't need a fancy charge controller to do this. Just limit the current with a resistor in series, and monitor the battery voltage during charging. Stop charging when it reaches 4.2V. This will get about 80% charge into the battery - enough to fly the drone. If you limit current to less than 1C then the battery will get more charge by the time it reaches 4.2V, but take longer to do so.
WARNING: you must not let the battery voltage go above 4.2V, or it will explode and set fire to everything around it! This is why a lipo charge controller is mandatory. If you do it manually then you are the charge controller, and it is your fault if the battery explodes.
So what resistor value do you need? During charging the battery voltage will raise from ~3.7V to 4.2V. The resistor must drop the difference between the battery voltage and the power supply voltage. So 5V - 3.7V = 1.3V, / 0.39A = 3.3Ω. As the voltage rises to 4.2V the current will reduce to 5V-4.2V = 0.8V, / 3.3Ω = 0.24A.
But perhaps you only have a 10Ω resistor? In that case the charging current will vary from 130mA to 80mA, and the battery will take
about 4 hours to charge. During this time you must regularly check the voltage to make sure it doesn't go above 4.2V - or the battery will explode! Now you see the advantage of using a proper lipo charge controller.