Looks like you can get 5.1 OmniROM for your phone. I just through a similar procedure for an older tablet.
http://forum.xda-developers.com/galaxy-s-i9000/i9000-development/rom-t3054101The usual caveats apply.
edit: The tools used to upgrade are usually written for Windows. I tried with Windows 10 and found it a frustrating/futile exercise for 2 days. In the end I used Windows 7 and was done in 20 minutes. Normally, I run Lubuntu, but there are usually no tools written for linux.
Additionally, a lot of these 3rd party ROMs are "one time" deals. After they are released, it is rare that they are updated with the latest Android monthly security patches. Running 5.1 is more secure than 2.6, but one could argue that is a false sense of security.
As such, I don't use any "smart phone" for any banking, email, etc. In addition, I usually create a "throwaway" email for these devices.