Transformers and power supplies can have partial failures. Computer power supplies usually do fail all the way, but not always. They don't always just die. Sometimes one set of windings can fail. For example, the windings for the 5v may fail, but the 12 volt windings are still working. Or a part on the circuit board may fail.
I would say 5 years for a high-use computer is good. Anytime after that, the power supply could be suspect. Any decent PC shop can diagnose it easily. I have a 10 year old PC (amongst others). That computer is on its 3rd power supply. The previous 2 supplies had full failures. They were real easy to diagnose.