How can I upgrade Safari?

Several sites are now telling me to upgrade Safari. My iMac is late 2006, I'm running 10.7.5, and my Safari is 6.1.6. From what I can glean, I can't upgrade Safari without upgrading my OS. Can I upgrade to 10.8 or above and solve my Safari problem? Is my hardware too old?

Has invited:

howapple - hello

Favor from:

1. Not on that Mac. Switch to a product such as Firefox.

2. Yes.

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