mac 10.10.5 browsers
Is there a secure browser like Brave that I can use on this mac 10.10.5?
MacBook Pro 13″, OS X 10.10
All Chromium based browsers now require using macOS 10.11+. You should be able to upgrade your Mac to at least macOS 10.11. Depending on the exact model of your Mac you may even be able to upgrade to an even newer version of macOS. See this article for a compatibility list of Macs and compatible operating systems:
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
Firefox now requires at least macOS 10.12+.
Maybe there are some Chromium or Mozilla based browsers which backport changes, but it is much easier to upgrade the OS to the lastest supported version so you can run the latest versions of the popular browsers.