Re armageddon, there is sometimes bidding ("how much time they're willing to give up to play with their desired color") instead of pre-determined 5min vs 4min.
What happens if the bid is drawn?
Chess Stack Exchange is a question and answer site for serious players and enthusiasts of chess. It only takes a minute to sign up.Sign up to join this community
Depends on the rules being used. A likely scenario is that an additional tie-break would be used.
For example, in the regulations for the 2016 US Championships:
If both Players bid exactly the same amount of time, the Chief Arbiter will flip a coin to determine who shall choose their color.