How much clock asynchronicity can secure protocols tolerate?

I've noticed that connections to a secure server got reset if time is out of sync on a server.

I believe time synchronization protocols can be just as precise to the order of network latency with the external time servers, which could be as much as few hundreds of milliseconds.

What are the time precision requirements of TLS connections and certificate validation?

I've heard 5 minutes thrown around several times as per EEAA's comment, but I honestly don't know why (and am looking forward to an explanation).

Bear in mind this is not the TLS protocol itself that has this precision-requirement, as per the documentation:

Clocks are not required to be set correctly by the basic TLS protocol; higher-level or application protocols may define additional requirements.