Fred is correct on the age issue. The general rule of thumb is 7 years but that is truly based on tires that are primarily exposed to outside weather. If a car is stored in a garage when not being driven and the tire pressure is monitored and maintained etc; that time frame of 7 years is not a 'firm' rule.
Also the driving expectations: if Gizmo had a set of 8 year old tires that had seen the 'worst case exposure' lifetime use I would guess he could rip them up in a weekend but for most of us, our cars are babied, garage kept and we are not driving them crazy hard constantly I would not worry about replacing them entirely based on age at 6-7 years but likewise would not run on 10 year old tires either.
FOR SALE: Having said all of that, I have a set of OEM run-flat take offs that have around 8500 miles on them that were removed shortly after I got my car in 2011. They have been stored indoors since then in an unheated garage. I am still in Florida so I can not check the date stamp on them. I am asking $500.00 for the set of 4 plus shipping. (I live in southern Ontario Canada but could ship from Niagara Falls, New York)