Since Apple transitioned to a unified release model, the Mac App Store typically only serves the latest version (currently Logic Pro 10.7.x or 11.x depending on your macOS). However, Apple does allow you to download older versions if you have previously purchased them.
The following methods are not proper and pose security, legal, and stability risks: download logic pro 10.5.1
Launch the App Store application on your Mac. Since Apple transitioned to a unified release model,
If you cannot legally download Logic Pro 10.5.1 because you never bought it or your Mac is too new, you have excellent alternatives. If you cannot legally download Logic Pro 10
You cannot buy 10.5.1 directly anymore. You must purchase the current version (roughly $199.99 USD). Once purchased, you may have limited ability to download older versions if your macOS is too old to run the newest one. Apple’s servers will automatically serve the "last compatible version" for your operating system.
To attempt to get 10.5.1: