I would say it very much depends on how you drive and how the car is stored when not in use. In theory, tyres older than 5 to 7 years harden off and become not only less grippy but also stiffer and less compliant, so it's a good idea to change them especially if you drive enthusiastically or in wet conditions. If you have any intention of driving near the limit eg on track days, then it's a must.
On the other hand, it's exposure to daylight that is the prime reason for tyres to harden, so if your car is kept in a garage when not in use and you drive in a touring rather than sporty manner in good weather, then it's tempting to leave them on the car.
I have a set of Vredestein Sprint Classics on my car that are now over 10 years old. I've been telling myself to change them for a couple of years now, but every time I go out in them I am unable to provoke them into losing grip unless I really try hard and there is no sign of degradation on the side walls so I've given them another year. They are definitely on my list to do something about this year though.
Bottom line: If you can afford it and are concerned, then change them, no question. If like me they seem ok, you don't thrash them, you don't want to fork out £400 unnecessarily, and you are happy to accept the risk, then you could consider leaving them a while.
