What is the business purpose of scheduling two separate flights on the very same route with 5-10 minutes separation? As in question. I have noticed, for example, that Berlin-Tegel has TXL-CDG route served by both AirBerlin and AirFrance with exactly five minutes separation. First plane takes off at 09:50 and second one at 09:55. I have also noticed that the same rule goes for longer routes, i.e. LHR-SYD goes with around 20-40 minutes separation, served by both Qantas and British Airways.

Can someone explain me a business or economic reason for doing so?

Why these two planes are not scheduled with a bigger separation? I.e. 2-3 hours or even half of day in case of long routes? Wouldn't that assure bigger chance or getting more customers? If route interest is big enough that two planes, near each other, needs to be scheduled, then why simply one airline don't use a larger airplane and the other one schedules its own flight 2-3 hours later or so to capture "other part of day" travellers?
If you look at just the schedules it says nothing. If you look at the prices you can see that Air Berlin was pricing the flight significantly lower than Air France. As was stated above, it was competition.

Unfortunately, things did not end well for Air Berlin. The airline declared bankruptcy in August 2017, and was unable to obtain further funds from its primary shareholder, Etihad. The company closed its doors in October of the same year.