iMac G5 - installing 2.5" SATA disk internally

It is not worth it, to spend money upgrading that old of an iMac.

If you are set on upgrading, OWC sales a 3.5" to 2.5" drive adapter and 3G SSD kit.

https://eshop.macsales.com/upgrades/imac-g5-17-inch-late-2005-1.9-ghz/InternalDrives?

https://eshop.macsales.com/upgrades/imac-g5-20-inch-late-2005-2.1-ghz/InternalDrives?

Plus some SSDs may not even be compatible with such an old system. Most current SSDs utilize a SATA III controller which should be backwards compatible with the SATA I controller in that old G5, however, some SSDs have trouble negotiating the SATA Link Speed with some older SATA Controllers. This is why OWC still makes the OWC Mercury Electra 3G SSD which utilizes a SATA II Controller. As @den.thed mentions, OWC sells everything needed for an SSD upgrade along with a compatible SSD.

I'm surprised that iMac is still running. Those G5 iMacs tended to have huge failure rates with the Logic Boards & Power Supplies due to the Chinese capacitors used in many of those systems which tended to bulge & leak causing power stability issues. Plus I believe many of those LCD Panels developed issues as well.

From history, Macs that had serious display issues from that period usually have the facility code "W8" at the start of the serial number. If you have a W8 Mac, I would not spend a nickel on it today.