While it is true that there is no law about tyre ages, a bit of common sense also has to apply - an old tyre can look new but still fail.
By way of a personal experience - I had a set of unused tyres stored in a dark room for a number of years and put them on my car mid last year. In early October I got a thump, thump, thump while driving along, when I pulled up this is what greeted me.
Note the tyre had not actually deflated but had delaminated. It had only covered about 1000km and looked brand new.
Also I believe someone returning from the Corowa Swim-In a few years ago got killed in his Land Rover due to a tyre blowout of an old military tyre.
All I am suggesting is that a visual inspection is not necessarily a good bench mark and maybe erring in the side of caution is.
Garry