Yes, you can use that same catalog. However, when switching from Lightroom 4 to Lightroom 5 a new copy of the catalog will be created in the format compatible with Lightroom 5. But you can certainly start with your Lightroom 4 catalog.
what must i do, step by step, to port my previous catalog to my new com,puter and put it into LR 5 which i have not yet installed?
1. Copy the entire folder that contains your catalog to the new computer. You can do this by copying the folder to a flash drive and then take the flash drive to the new computer.
2. Install Lightroom 5 on the new computer.
3. Double-click on the Lightroom 4 catalog that you have been using. Lightroom 5 will recognize that it needs to be updated and will proceed with the update process. When that process is complete you should be able to go to work with Lightroom 5.
To make the transition as smooth as possible, you need to ensure that your external hard drives have the same name or letter designation that they had previously. Otherwise, you will have to find what Lightroom will consider missing folders. It's not a big deal, but it's easily avoided if you have your new computer set up properly.