Doesn't sound like many people here have experience with older tires, here's mine:
I've tested with my cars and other volunteers' cars various tires that are between 6 and 15 years old(surplus inventory that has been in storage for a few years). So far zero have had blowouts. Only one problem came up, and that was one tire that had a repair patch that came undone which caused a rapid leak, and the driver simply pulled over to the side of the road and mounted their spare.
One issue I've noticed with the older tires is that they have increased road noise, wear rates, and slightly reduced grip compared to new. All tires were either high performance summer, max performance summer, or extreme performance summer; all of which still had significantly more grip than an all season tire.
Tire cracking was not dependent on tire manufacturer or tire age, but was dependent on exposure, such as water, chemicals, UV light, and extreme temperatures. Some older tires of a same model looked fine, while some newer tires that had spent more time outside showed some cracks. Occasionally tires can show small cracks and after a little bit of driving simply go away as they were only in the very top layer of the rubber.
My conclusion: If the rubber is still black and shows minimal to no cracking, I wouldn't worry about it. It's a relatively common thing for tires on cars that aren't driven much, not driven hard, and are kept garaged. A tire that has rubber turning brown from oxidation and/or is showing cracks I would take note and not do any hard driving, 100+mph driving, or carrying heavy loads. If cracks are visibly going deep into the tire, can be felt, more form if you deform the tire, or any bad vibrations can be felt I would throw the tire away. If the condition of your tires is ever questionable to you, and you believe your tires can put your money or anyone's safety at risk, I suggest replacing them. Going by age is a bad judgement, since some tires can literally be made unsafe without any physical damage in less than a year, and a properly cared for tire can easily last 10.
Tire brands tested include: Yokohama, Michelin, and Continental.
Cars tested on include: Porsche 996 Carrera, BMW E46 M3, BMW E46 non-M, BMW E28 5 series, Mercedes-Benz 190E 2.3-16, Mercedes-Benz first generation ML430, Ford fourth generation Mustang.