I have an old iMac with Yosemite 10.10.5 and safari won't access many sites. Any way to update it?

I got hold of an old iMac with Yosemite 10.10.5 with the intent of using it as a server to hold photos, etc. that would be access over our internal wireless network. I've established the connection from my new MacBook Air and that's working pretty well.

However, playing around with the iMac, I tried using Safari and being back level, it's having certificate problems accessing some sites -- even the Apple Support site returns a message telling me I should consider downloading Chrome, Firefox, etc. I tried that and both tell me my OS is too old.

So, just wondering if anyone out there has any ideas as to how I might improve upon the iOS or at least find a web browser that will allow me access to things that I simply can't get to on that machine as it is today.