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.

The inverter has a software delay. This is intentional.
It waits 5 minutes to make sure it is connected to a stable grid.

An inverter could theoretically connect and go full power in seconds. But it doesn't. For example, if after a power failure, all inverters immediately went online a started outputting full power, the network would be overwhelmed and will fail again due to overspeed.

Instead, it waits for a stable mains connection. Since it can be less stable after a large scale failure, when there is still a lot of switching going on.
And then slowly ramps up the power in a controlled slope.

Some regions have specific regulations for inverters, see your local grid code.