Not a lot of helpers left here who used PPC Macs. I have.
If a fan stops working, or an internal temperature sensor fails, the remaining fans will go to full speed to compensate.
If you still have the optical disks the shipped with the Mac, find Apple Hardware Test on one of them. It is quite good at picking up sensor and fan motor problems which, from your post, are high on my suspect list.
How to use Apple Hardware Test on your Mac - Apple Support
⚠️ The only option you have is the version on that optical disk. The "hold D at startup" option is too new for an G5 and the downloadable versions of AHT never worked right. If you don't have the disk, your chances of getting this properly diagnosed go down,
If you have the disk and AHT throws out error codes, please post the codes here, They are hard to translate but I know that codes starting with 4SNS are sensor errors and those with 4MOT are fan errors. For sensor codes, posting the entire code will show what kind of sensor is acting badly.
Have you tried booting in Safe Mode? That may help with software and storage issues. Hold SHIFT until you get a workabel desktop, which can take a few minutes. Once ins Safe Mode, let the computer sit for 20-30 minute while Safe Mode does all its checks anfd any needed repairs.
For fan issues you can also try resetting the System Management Unit, or "SMU." Finding it may depend on your G5's sub-model. This outside article many help: https://thedesignspace.net/MT2archives/000447.html
⚠️ Press the button only once and for no more tha a second. ⚠️ Longer presses or multiple press could turn your G5 to scrap.
