No, you do not have to re-install everything. When you get your new 500 GB HDD, go to the website of its manufacturer. There look for a free disk utility package to download and install on your C: drive that includes software for CLONING. For example, for a WD hard drive get their Acronis True Image WD Edition; for a new Seagate HDD, get their Disk Wizard. Make sure you also get and READ the user manual document, especially the section on how to clone.
A cloning tool can copy absolutely everything from your old HDD to the new one, making sure that the new one is completely bootable and able to take over the job of being your C: drive that you boot from. You start by installing your new HDD in your machine and running the cloning software. When you use it the FIRST step it to identify the SOURCE drive (make sure that is the old smaller unit) and the DESTINATION drive (MUST be the new unit - this one will be wiped clean!). It will show you what it plans to do in terms of making new Partition(s) on the new unit to accept all the data from the old one. Look this over carefully and make sure that it will use up ALL of the space on the new drive. (Some older cloning tools I have used wanted to make the Partition space on the new drive the same size as the old one, and that is too small!) IF you think the proposed plan is incorrect you can use the menu choices to alter the plan - that is why I said to READ the manual to know how if you need to. When the plan is correct, tell it to go ahead.
When the cloning is finished, back out of the software and shut down. Now open the case, and exchange the SATA data cable connections between the two HDD units. This way the NEW larger HDD containing the clone will be connected to the same mobo SATA port as the old one WAS, and the old smaller unit will be on a new SATA port. Close the case and boot up. You should find that it all works just as before, except that your C: drive suddenly is bigger - just what you want. You also will find that there is a second HDD under a different letter name, and it's your old one with all its data. If you want, just leave that alone until you are convinced that your new larger drive did get everything.
When you are sure you need NOTHING from your old HDD, start up that disk utility again. Make SURE you tell it to work only on the old smaller HDD. Now use its tools to Delete any and all Partitions on it so that it is completely empty. Then Create and Format a new Partition that uses ALL of that disk's space (this may be called Initializing the drive, or Creating a New Simple Volume), and it does NOT need to be a bootable drive because it will only be for data storage. Whne this is finished, back out of the software utility and reboot. Your system will be like before, except that the old drive now will be all empty Free Space that you can use for storage.