All of a sudden both Microsoft and Apple have decided to release new versions of their operating systems that do not support older system. In the case of Microsoft, Windows 11 is not going to support older hardware. Similarly, Apple has released macOS 11.5 “Big Sur” that cannot be installed on older Macs.
However, if you want to upgrade your older Mac to the latest version of macOS (which is macOS 11.5 at the moment), then you can use an open-source tool called Patched Sur. As you can probably guess, this tool can make come changes to the system files which allows the upgrade to macOS Big Sur go through without any problem. You can find which of the Macs this tool supports from https://bensova.gitbook.io/big-sur/supported-macs/.
Using Patched Sur is very easy. First of all you have to update your Mac to the latest version as much a allowed by Apple. After this download Patched-Sur.dmg and double-click on it. In the small window that opens, double-click on the Patched Sur icon and it will take care of the rest. You may have to pick a few options such as which version is going to be upgraded to Big Sur. After this, it will create a USB drive which is going to used as installation drive for macOS. This step takes a long time as it has to download the installation files.
For finishing the installation, you have to boot from the created USB drive and continue with the macOS Big Sur installation. After the installation is done and you have logged in, you may want to install Post-Install-App.dmg which is also available from the Patched Sur GutHub page. This app allows for convenient updates in the future.
The process seems very straightforward, but since it is not officially supported, it might not work on your Mac. But if you really want to upgrade to Big Sur, it is definitely something to give a try.
You can download Patched Sur from https://github.com/BenSova/Patched-Sur/.