For the record, I myself use TenFourFox for my banking and
credit cards. TenFourFox supports the latest encryption and
security methods, including TLS 1.2 and SHA-256 certificates.
However, remember that any use of TenFourFox, secure or not, is
always at your own risk.
Power Macs running 10.4 and 10.5 do have known security holes.
They are much less likely to be exploited because of the unusual
nature of the PowerPC CPU, but they do exist. You should make sure
all system patches are installed, never use Flash or Java on your
computer, and always connect to trusted networks or Wi-Fi
In addition, you can use TenFourFoxBox
to create a special private instance of TenFourFox for your bank's
website. This will hold personal data separately from the main
browser, reducing the risk it will leak to a malicious site.