5.7 catalog new compter m1 chip

The only way for you to access that catalog would be for you to subscribe to the photography plan and install Lightroom Classic. After you install LrC it will find that catalog and prompt you to upgrade it. The upgrade process will create a new copy that will be compatible with Lightroom Classic. All of your work will be in the old process version, and you will have to decide whether or not to update the process version or leave the old work in the old process version. Changing process versions could affect the appearance of some images. New imports will be imported at the current process version.

Well, a new Mac would run Mac OS 12 (Monterey) with no option to go back. So you couldn't run Lightroom 5.7. You'd need a current subscription to "Lightroom Classic", the version today is 11.3.1. You cannot go back before version 10, perhaps not even that far on Monterey. Whether it can use that external catalog would be a question for the Lightroom Forum. You will need internet to download the software, which may be painful to download.