As usual, Cory offers excellent advice. I'd like to add a couple of comments.
First, assuming your current internal drive is a hard disk drive, it would be possible to replace it with a 750 gig SSD. I suspect that your current drive would fit inside a 2.5" external enclosure, as would the SSD. When I replaced the 1 TB hard disk drive that was inside my Mac Mini with a 256 gig Samsung 840 Pro SSD, I was able to install that 1 TB drive inside a 2.5" external case, and it has come in handy whenever we travel.
I'll describe what I did with the swap, although it could be somewhat "different" than what you would do. I first purchased both the SSD and the 2.5" external enclosure. I then attached the SSD to my Mac Mini, and used Disk Utility to Erase and Format the SSD (only one partition is all I needed). After I did my usual disk cleanup/maintenance/repairs on the internal drive, I made a SuperDuper! backup to the SSD. SuperDuper! makes an exact, bootable clone of what is on your drive. I then rebooted my Mac Mini from the SSD, and it worked fine. I subsequently shut everything down, unplugged the Mac Mini, removed the SSD from the external enclosure, opened up the Mac Mini and swapped the drives, closed the Mac Mini, and successfully booted it up. I then installed the 1 TB drive inside the external enclosure.
In your case, assuming you do not use the machine at all, you would still first purchase the 2.5" external enclosure (with a USB 3.0 port) and the 750 gig SSD. Now here is where I am unsure how you would proceed, assuming you will not use SuperDuper!. Time Machine does not make a bootable backup. There should be a file entitled "Install OS X "OS Name"" inside your Applications Folder. For example, on both of my machines, I still have the file entitled "Install OS X El Capitan" inside mine. If you connect the external enclosure containing the 750 gig SSD to your Mac, you would first (as I did) use Disk Utility to Erase and Format the SSD. You would need to decide how many partitions you need, but let's say you make 3 partitions. I would think you could launch that "Install OS X "OS Name"", and perform a clean, "virgin" installation on one of the partitions on the SSD. You should then have an exact "copy" of what is on the 500 gig HDD. You can test this by restarting your Mac from the external SSD.
Even if you first use the machine "a little bit", you could also us Migration Assistant to transfer any of the extra files created due to your use of the machine.
Finally, you would then close down everything down, remove the 750 gig SSD from the internal enclosure, open up the MacBook Pro and swap out the 500 gig HDD for the 750 gig SSD. You could then install the 500 gig HDD inside the external enclosure and use it for storage, backups, etc. I have two partitions on my 1 TB drive. One I use for backing up my MacBook Air right before we go on a trip, and the other partition contains a bunch of "stuff", including a number of moves and TV series.
As Cory stated, you need to let us know the exact MacBook Pro model you have. With that information, we will be able to provide the link to the part of the ifixit site that will show how to do such a swap in a step-by-step fashion.
If instead you decide to go with an external 750 gig SSD, keep in mind that such drives with a Thunderbolt interface are expensive. In actuality, you could go the route I stated above (purchase an external enclosure with a USB 3.0 interface, along with the drive), and set up the SDD as a boot drive (again as I described above). The drawback, though, will be that it will be slower than using an enclosure with a Thunderbolt interface (assuming your MacBook Pro has a Thunderbolt port).
