I have been doing some dodgy experiments towards measuring the battery charging current. It will be difficult to clearly define the value in km. First of all, you did not write what battery and what car it is.
Personally, I think (I can be wrong, of course) that the car installation (read alternator) treats our battery neglectfully, because the regulator maintains a constant voltage in the electrical system. Imagine a situation when you spin for a long time to smoke. The battery will be deeply discharged, i.e. its voltage will drop (e.g. to 12V). When the engine starts, the voltage in the installation will be, for example, 13.8V. This means that the charging current can amount to several dozen amps (measured in VW Golf). Of course, such a current will flow to the battery for a short time, then it will decrease (after two hours of driving, the charging current for me was less than an ampere - so you can take the eye five times that the battery was charged - my mistake was not measuring the density of the electrolyte).
You need to approach the topic like this: first, we unload (start) the battery. The "size" of the discharge is the starter current times the turning time. Then the battery is charged from the alternator - this is also electricity times time.
As both currents are hard to tell, it will be hard to tell the time (which is your kilometers) to charge.
A lot will depend on whether your car is smoking on a tick or you have to spin a minute.
Certainly, a 5-minute drive (5 km) is not enough to fully charge it. The best solution will be your own experience. Light up in the morning, drive 50 km, and after an hour measure the electrolyte density. The battery is fully charged when the electrolyte density is 1.270 - 1.280 kg / L. Sorry for the long talk, but I wanted to explain it somehow.