I have a Mac 21.5 Mid 2010, I need to update my safari browser, can I do this?

If you are running macOS 10.13, then you can instead use a third party browser such as Firefox, Google Chrome, or Vivaldi. Sooner or later even these browsers will be unsupported, unfortunately we don't know how many years they will be supported.

No. Safari is part of macOS. That machine can’t run a version of macOS higher than 10.13.6. If you’re up to date on macOS, that’s as far as Safari can go.