Is a Macintosh G5 PC worth updating?

Just to note, it can't be a G5 with an Intel CPU. G5 refers to the 5th Generation PowerPC CPUs used before Apple switched to Intel.

With only 4GB of RAM, it isn't going to be usable for much. And a boot time that slow says the drive is most likely a molasses slow 5200 RPM unit, and maybe failing at that.

OS X / macOS is written essentially as a GUI on top of what started as the Berkeley UNIX release. It's no longer even in the same category as Apple's engineers have written hundreds of UNIX modules that only exist in the Mac OS.

Catalina and later were also written to run best on an SSD. On a slow spinning hard drive, it's going to be slower just for that, besides the lack of RAM to run Monterey well.

I personally wouldn't invest the money to try and speed it up.

That Mac is too old to receive repairs from either an Apple Store, or Apple Authorized Service Center. Apple no longer makes parts for it either. If it is a G5 Power PC processor, then you are definitely not running Monterey on it. I would not spend a cent on it, and after saving any files on it that you want to keep, I would scrub the drive and give to Apple to recycle for you.

That makes it somewhat simpler. The hard drive is a chore to upgrade as it takes a fair amount of disassembling to get at it. But the RAM on that model is easy. Turn it over, take off the black, bottom plate, and switch out the RAM modules.

A 16 GB upgrade set is $67 at OWC.

https://eshop.macsales.com/shop/memory/Apple/Mac_mini/DDR3_1600

Mind you, that Mac still won't be able to run any OS later than Catalina, but it would certainly run better than it is now. And then it depends on what you think you'll be using it for to determine if it's worth the $67 cost.

Any slowness you see is likely not due to RAM but to a slow mechanical hard drive. Adding RAM will not make any noticeable difference in speed. Only replacing the old HDD with a solid-state drive (SSD) will make any perceptible speed increase in actual use. See:

https://eshop.macsales.com/item/OWC/YSSDMP500/

Here are data showing showing progressive changes in launch times for my two most slow-loading apps as I first doubled the RAM, then changed the factory mech HDD for an SSD. This is a 2012 Macbook Pro with the same 2.5ghz processor as your Mini:

Base system as shipped:

4GB RAM and factory SATA 3GBps 5400rpm HD: Office 2008 and Photoshop Elements 12 took 15-18 seconds to be ready to use.

First upgrade, double the RAM:

8GB RAM and slow SATA 3GBps 5400rpm hard drive: Office and Photoshop Elements took 15-18 seconds to be ready to use.

Second upgrade, inexpensive solid-state drive

8GB RAM and fast SATA 6GBps SSD: Office and Photoshop Elements take under 4 seconds to be ready to use.

So what made a difference?