USB wifi connectivity on 10.5

With that old of an OS, it's unlikely the wifi dongle you bought will work. It for sure would need a driver/software to be installed.

The best option would be to hardwire the Mac to your router.

What model of USB dongle did you buy?

~Lyssa

At the risk of muddying the water here a bit, I found this old c/net article online regarding:

AirPort problems in Leopard (Mac OS X 10.5) - CNET

If you are certain that your machine does not have an AirPort card installed, then certainly just disregard the article.

On a different track, I wonder if an old AirPort Express connected via ethernet to your Power Mac might not get you hooked into your wireless home network.

Yes, as Lyssa indicated, USB Wi-Fi adapters with Mac drivers for older operating systems can be difficult to find. For example, Edimax EW-7811Un and ASUS USB-N53 do still have drivers for Mac OS X 10.5 available on their respective support/download web pages (but you may want to check whether these drivers actually work with the exact adapter hardware versions).

A better alternative could be to connect a wireless Ethernet bridge to the Ethernet port of the old Power Mac. There are dedicated bridge devices (also known as gaming/entertainment/media adapters, such as Linksys WET610N and Netgear WNCE2001), but it may be easier and less expensive to use the wireless Ethernet bridge mode in some Wi-Fi range extenders (like Edimax EW-7438RPn Mini or TP-Link RE200). A wireless Ethernet bridge does not normally need special drivers, so almost any operating system can be used. One would typically configure the bridge via a standard web browser (if necessary, using another computer).