I keep getting notices that my safari (5.1.10)is unsupported

Safari is a part of OS X and each version is upgraded as you upgrade your operating system.

The most recent (current) version of Safari is 8 and it's a part of OS X 10.10.2.

Your OS is so old that the only way to browse securely is to upgrade your OS or use a different browser such as Firefox or Chrome.

Backup your data.

Check to see if your iMac will support Yosemite. If you don't know how to do that post as much information about your iMac was you can and ewe can't figure that out. Once you know what version of OS X your iMac can support,we can help you with a plan to upgrade to it.

I have kept 10.6.8 as well and everything eventually moves on making things obsolete.

So many things are now bursting with the latest technology and the old software cannot handle it. Once a certain point is reached those writing and utilizing the tech in business see no advantage in accommodating the weakest applications.

You should start planning to upgrade to a computer system that is at least more up to date if not current.

If you do not want to upgrade your OS X version JUST to get an updated web browser, do a web search for, download, install and try

Mozilla FireFox.

The current, up-to-date version of FireFox is fully compatible with OS X and is regularly updated by the great developers of the Mozilla group.

MichelPM wrote:

...Mozilla FireFox.

The current, up-to-date version of FireFox is fully compatible with OS X and is regularly updated by the great developers of the Mozilla group.

FWIW I have experienced problems with the last three updates of Firefox. I routinely have to Force Quit the application. However, it may not have anything to do with being at the lowest end of the OS compatibility list.

I am still using OS X 10.6.8 and have had no issues at all with any FireFox updates.

Check your FireFox extensions/add-ons to see if they are updated to latest version or have become obsolete, in which case, you need to delete/uninstall the problem add-on/s.