Samsung Galaxy S3 Software Update 5.0 Free Download =link= -
The never received an official Android 5.0 Lollipop software update from Samsung. The final official operating system for most variants remains Android 4.3 Jelly Bean or 4.4.2 KitKat for specific 2GB RAM models. Official Update Status Final Official Version: Most standard models ( Go to product viewer dialog for this item. ) are limited to Android 4.3 Jelly Bean
This process voids your warranty (already expired), wipes your data, and carries a risk of bricking your device if done incorrectly. Proceed at your own risk.
You must install TWRP (Team Win Recovery Project) or CWM to flash the new software.
Since the S3 is over a decade old, warranty isn't an issue, but you do risk "bricking" the device if the installation fails.