iMac No longer provides updates

My moms imac needs new updates and is still running version 10.5.8. We got it around 2009 and is still running mostly old versions of applications.

2.8 processor speed 2 gb RAM 500 gb harddrive not even using 100gb currently.

The only updates it gives are for bluetooth and itunes.

safari is still running a 5.0.6 version

Please help me figure out how to get this computer updated to current standards