Just as a counter-argument (and, to be clear, I do support raising our minimum version), just because PHP has EOL'ed a version does not mean that some distributions (esp. Debian, Ubuntu) are not providing additional support and security updates.
If I remember from the last time we had this discussion, it will still be a couple more months before PHP 5.3 is no longer supported by most major distros, and it will be a while before 5.4 is no longer supported.
-- Tyler Romeo https://parent5446.nyc 0x405D34A7C86B42DF