The question doesn't say how much is ON your 500 gb drive. 500 gb is the total it can hold.
I don't know your computer knowledge level, so don't take offense if my answer includes info that you already know. I'm writing so that even a "newbee" to Macs can understand.
Single click on your hard drive icon on your desktop and hit command "I". (or go to the top of your screen and click on Find. Then click on Get Info in the menu that opened when you clicked on Find.)
The little window that will open is the info for the drive. You need to look at the number after the word Used. If it is under 300 gb, no problem doing a backup.
Note that the number after the word Capacity will be lower than 500 gb (just as a "Get Info" for your 300 gb drive will show a capacity less than 300 gb.) The rest of the drive is used for formatting, etc. and not usable by you. IE: My 250 gb drives actually have 233 gb usable capacity and my 1 tb drives actually have 933 gb usable.
Also "Get Info" for the 300 gb drive and check to see if it says Mac OS Extended (Journaled) after the word Format. If it isn't already formatted for Mac you should reformat the 300 gb drive to Mac OS Extended (Journaled) for the best compatibility when doing a backup.
If it is a different format, the next paragraph explains how to format a drive. Note that formatting a drive erases any data on that drive, so make sure there isn't anything on the drive that you want to keep.
To format/partition a drive, open your hard drive, open Applications, open Utilities, open Disk Utility. (It may be called Disk Utility.app) Select your 300 gb drive from the drives on the left side of the window. (there will be at least 2 listings for each drive in the list. The top one starts closest to the left edge of the window. That is the entire drive and the one to use. The one(s) under that are the existing partition(s) on the drive.)
Select Partition at the top of the right side of the window. (It will not be an available selection if you have selected a partition instead of the entire drive.) Now select a single partition, give it a name, select Mac OS Extended (Journaled) from the Format menu and click on Partition at the bottom of the window. Let it do its thing until it is finished. Check the drive to make sure it formatted properly by clicking on Verify Disk at the bottom right of the window. It doesn't take long to verify an empty disk.
what the hell do u think?
Are you using ALL the 500GB on the Mac? if so then no it won't work unless you compress all you files.
are you retarted?
i mean you can't do it even after you compress it