The iMac G5 is prone to blown capacitors. This is typically the problem on many iMac G5s.
To make sure the caps aren't bad, get an ESR meter and check the caps. You may need to scrape the conformal coating off of the board but it is possible to access the leads for the caps. If you can, desolder the caps and check them off of the board; bad caps can screw up in-circuit reading.
As far as the tolerance goes, it's best to rely on the manufacturer datasheet. Good ESR meters generally include a ESR chart, but this is approximate.
If you replace the caps and it's slow, the hard drive is failing. As a general rule, these drives fail in 4-5 years. Many drives live past this, but there's no guarantee how long it will last beyond 4-5 years. It's a good practice to retire older drives with higher hours before they fail, since you can move the drive to another system that's less critical.
If you continue having problems, just replace the system. The iMac G5 is a piece of crap as a whole. They are prone to bad caps, excessive temperatures and display TAB problems. All of this is compounded by a TDMS panel, which is nearly impossible to find and difficult to replace since the machine looks for an Apple display EDID (without an injector). Apple has stopped selling parts for these machines years ago, so whatever is left is generally on life support and is prone to CCFL backlight burnouts or higher TAB failure rates.
From the beginning, the G5 iMac was never very good. They were fine early on but degraded quickly as they aged. ANY surviving machines will fail due to caps or display issues, given a few more years. I'd get a Intel iMac and cut your losses on this one.