Trouble with some websites opening in Safari

I have OS X Yosemite 10.10.5 on my MacPro Retina mid 2014. In the past month, I have noticed some websites cannot be found or pictures will not appear on the website. When I use Google Chrome on the same device, the issue resolves itself. I do not have a lot of space to update to the latest OS X. Should I update to a more recent program, need a new computer, or delete what I can and update to the new? Would I have a setting on that I am unaware about? Please leave detailed suggestions because I am unfamiliar with a lot of software technology.

Safari on my XS phone works fine so that is why I think it is the program rather than the device.

Thanks for your suggestions!