From my understanding, the 5 mins limit at take-off thrust is actually an EGT time limit.
For instance, the CFM56 engine (A340) has a EGT limit of 950 for up to 5 mins. For any lenght of time exceeding 5 mins, the max EGT allowed is 915. So whether it's Flex or Toga, one must reduce to MCT or less after 5 mins in order not to exceed 5 mins with an EGT over 915.
The AMM has a chart depicting the maintenance actions required in relation to the peak EGT and lenght of time when an exceedance as occured.