Now that MacOS Catalina has moved to zsh, can I upgrade bash 3.2.57 with 5.0.3?
You can't easily (and shouldn't) change/upgrade /bin/bash. You can install a more recent version of bash through Homebrew though, and use the information from How to use bash as default shell to change your login shell.

This will not break any existing bash scripts as these refer to #!/bin/bash in the first line.