It does highlight another potential issue when choosing Wordpress (or any CMS) over hard-coded HTML / JS / CSS. Most CMS systems are written in PHP, which is always being patched / improved itself. Your host should have given you warning (a LOT of warning, and a testing period where you could choose 5.6 or 5.4), but you can't halt progress and it will eventually force 5.6 (for "security" reasons, probably), at which point you'd better hope that Wordpress is compatible, as wlel as any themes / plugins you use.
Like I said earlier - when you choose this option sometimes things outside of your control mean you wake up to a broken site which requires your attention.
By the way - PHP 5.6 has very little impact on existing code when migrating from 5.5 (
http://php.net/manual/en/migration56.php), which suggests whatever you had that broke with 5.6 will not work on 5.5 either.