FIrst, you state your Mac is running 10.5??! Is that correct? That's an extremely old Mac OS X version. If that's correct then there is no upgrade path for you to macOS 11 Big Sur. The machine is much too old.
To be clear, software update generally means to install software to update the macOS currently running on the Mac; update Catalina 10.15.1 to Catalina 10.15.7, for example.
To update your current macOS, click the Apple icon > About This Mac and then click Software Updates.... If there are any updates available for your Mac, they will be listed and you can apply them when you like.
A software upgrade is usually a generational step up to a newer macOS; upgrade from 10.13 High Sierra to 10.14 Mojave, for example, or from 10.15 Catalina to macOS 11 Big Sur.
❗️ Do NOT upgrade until you have made a Time Machine or other backup of your startup drive.
Learn How to Back up your Mac with Time Machine
How to Upgrade macOS:
The macOS version you can upgrade to depends on the year your Mac was released.
Click the (Apple) menu at the top of your screen and choose About This Mac.
Check the Compatibility of your Mac with newer versions of macOS:
➡️ macOS 11 Big Sur is compatible with the Macs listed here
❗️ – IMPORTANT – Your 32-bit apps won’t work in Catalina or Big Sur.
https://support.apple.com/en-us/HT208436
Use the free utility Go64 to check the compatibility of your apps:
https://www.stclairsoft.com/Go64/
✅ - IF your Mac and apps are compatible, then using Safari only, download the macOS upgrade installer app:
Click > Big Sur.
Once downloaded, double-click the “Install macOS…” app in the Applications folder to begin the upgrade.