My friend lent me his computer, which I am on right now. It's a newer mac and has Lightroom 5. BUT it won't open my catalog from my hard drive because of some formatting issue.
What formatting issue?
What is the error message when LR 5 can't open your catalog file?
From this point forward, no matter what happens with your catalog, you need to commit yourself to making regular and automated backups of your catalog file and photos to a different hard disk than where the originals are stored. No excuses. This is mandatory.
The Lightroom (LR) catalog does not contain your image files. When piictures are imported LR moves a copy of the image files from the camera memory card to a folder location on your hard drive. If you do not specify a folder location they will be copied to the default Windows 8 'My Pictures' folder. That is where you will find your image files! The LR Catalog contains your LR Develop module editing settings for image file and any metadata tags you may have added.
Your LR 5 catalog will not open using LR 4 because it is an older version that does not support the new features. A Mac system will not be able to open the catalog with LR 5 since the external drive is probably NTFS formatted. You can however "read" the files on the external drive using Mac Finder. Check it and see if you can find your camera image files, which are probably in the 'Pictures' folder.
That laptop partially MELTED, and a friend managed to back up my hard drive to my external, which was obviously formatted for a PC. Here is where it gets tricky.
What do you mean by "melted?" Please explain the symptoms, what actually failed, and how the hard drive was copied over to the external drive.
As dj_paige has mentioned you should make regular backup copies of your LR catalog to an external hard drive. You also need to backup all of your imported image files in the 'My Pictures' folder or wherever you have stored them! I also suggest reading LR tutorials to get a better understanding of how "non-destructive" editing works with your image files. Here's a good place to start:
Read 'Importing Your Images' first and continue from there as needed.