Tyres degrade with age (they lose their suppleness and grip) and 10 years is about the useable limit depending on storage conditions, exposure to UV etc.
Personally I would replace them at this point. Tyres are the most important part of your bike, not something worth skimping on.

Another reason to replace them is that tyres have improved a lot compared to a decade ago. Depending on your frame clearance you will want at least 25c modern tyres.