Q: unable to access banking

Without knowing what OS X or Safari version you are using, it is highly likely that you are using outdated versions of both. You are going to encounter an increasing number of those "outdated" messages until you upgrade. To learn how to do that please read Learn how to upgrade to the latest version of OS X. It's free.

You don't indicate what version of Safari and what version of OS X you are running. You can find the OS X version by going to the Apple menu and clicking About This Mac and then click Overview at the top of the window that opens. You can find the Safari version by running Safari and then clicking About Safari on the menu named Safari.

In general (without knowing the specifics of your versions) Apple discontinues updates of Safari for a specific version of older OS X versions as time passes. For example, the last version of Safari for OS X 10.7 (Lion) was Safari version 6.1.6 and that was released in August 2014. Due to it's age and lack of updates it can be a security risk.

Your options are to update your OS X which will also update Safari or if you cannot or do not want to do that (do to possible conflicts with existing hardware and software) you could switch from Safari to Firefox. https://www.mozilla.org/en-US/firefox/new/

However note that Firefox will be discontinuing updates for older OS X versions in the near future: https://blog.mozilla.org/futurereleases/2016/04/29/update-on-firefox-support-for -os-x/

If your bank is Chase -- they apparently are having a new issue as I am using the latest version of OS X (10.11.5) and Safari (9.1.1) and they are giving me the "You need to upgrade your browser ..." message this morning -- encountered that about 1/2 hour after my previous reply. My other bank is OK.