Personally, that cracking would not stop me driving the car at all, but I would certainly check the tyre pressures before going anywhere and would not
drive it either fast or like I stole it....
You certainly need to budget for replacement tyres in the immediate future - there doesn't look to be a huge amount of tread depth, so new tyres wouldn't be a bad idea for grip in the wet, never mind those cracks.
You can tell how old a tyre is by reading the info on the side of the tyre - you are looking for a string of 15 letters and numbers starting with 'DOT'. Here is the one from one of my tyres:
It's the last group that give the manufacturing week - so my tyres was made in the 24th week of 2012. If yours are very old, it's possible that the code is only three numbers long - two numbers for the week and one for the year, so 011 would be the first week of 2001.
There are no hard and fast rules about how long tyres are safe to use, as most tyres wear out before they 'age out'. But at 6 years old, they are getting old and 10 years is probably a sensible maximum. It's ultraviolet that kills tyres so if they have stood outside all their life, that ages them faster than in a garage.