If you are upgrading to Lightroom Classic then all you need to do is install the program and run it. Lightroom Classic will find your Lightroom 5 catalog and prompt you to upgrade it. Agree to do that, and Classic will create a new copy of that old catalog that is compatible with Classic, and you should be able to continue working with no interruption, all editing that you completed previously should still be intact.
If you are upgrading to Lightroom, the new cloud-based Lightroom, then it will be necessary for you to install the trial version of Lightroom classic long enough to enable it to create that upgraded copy of the catalog. Then you will be able to migrate that catalog to Lightroom, and all your images will be in the cloud.
That is a very basic, beginning answer to your question. Feel free to ask further. Lightroom Classic is the version that works very similarly to what you are accustomed to. Lightroom is a newer version and isn't quite as feature rich at this time. My advice to you would be to choose carefully. Ensure that the choice you make is going to meet your expectations.