Thanks for your answers.
I will use the following strategy:
- if button is pushed > wake-up (interrupt) > Go in SLEEP_MODE_PWR_SAVE so that timer2 is active (1ms timebase from 32kHz clock)
- maintain a ms counter
- If button is pushed again > check the time difference with the previous time (timer2 reg)
- if after a timeout from 5min (processed from timer2 value) no button is pushed > go back in SLEEP_MODE_PWR_DOWN which will stop timer2. System is ready for next operation.
That way, the system is only active when waking up (either from pin interrupt or from timer2 and will allways sleep.
Optimisation: enable watchdog when waiting for next wake-up, to track time between 2 wake-up (but this is not needed for my needs)