Can I upgrade Safari past 5.1.10 with OS X 10.6.8?

I keep getting messages that my Safari is outdated and no longer supported by websites. I am directed to a lengthy description of the virtues of Safari, but there is no Update link. There seems to be a message hidden between the lines that I must have Yosemite in order to get any more Safari upgrades. If this is true why don't they just say so? If not true, how can I get a more recent version of Safari?