Why does inverter synchronization with the grid take 5 minutes?
It's nothing to do with synchronization. It has to do with ensuring safety of utility workers. The inverter should be quick to disconnect in the case of a grid failure (seconds) wait a period of time (in this case 5 minutes) after the grid is restored before beginning to supply power out to the grid. 

See, for example this exchange (the "standard" in question is  UL 1741/IEEE 1547). 


  Question: 
  
  I understand the requirement to cease energizing within 2 seconds. How
  long does the inverter have to be de-energized before coming up to
  provide power to a local load w/ the utility breaker open? 
  
  Answer: 
  
  The standard does not directly address it, but from a lab perspective,
  common practice is to have the inverter wait a minimum of 5 minutes
  after the Area EPS steady-state voltage and frequency have been
  restored.


Further comments indicate that some European countries require 3 minutes and Australia requires 1 minute.