Did you know that you can also consider running eZ Publish legacy side by side with eZ Platform, and that this is supported together with eZ Publish Enterprise? It provides new features and , simplified migration paths, fully supports PHP 7 (including 7.2 and higher), and can be a good alternative to 5.4 which does not receive new features anymore.
PHP 7.x series adds more and more deprecations to cleanup the language for each new release. As 5.4 is a stable release, and on has a legacy from way before PHP7 came, we can not risk BC breaks on 5.4 by attempting to fix these deprecations. However in the newer feature releases of legacy support for this is progressively being added by both eZ and the community, making upgrading to eZ Platform 2.x + legacy bridge + eZ Publish legacy 5.98 ("2018.x") a viable alternative if you are up for adapting your own extensions for changes in PHP.
So while we will try to make sure 5.4 is able to boot on higher version of PHP 7.x, it won't be officially supported for use in production. In practice this means if you hit issues which can be attributed to PHP version, and we can't fix it without breaking BC, then we will ask you to either upgrade eZ install or downgrade PHP.
eZ Platform, including platform parts bundled with eZ Publish Platform 5.x, was made for more recent versions of PHP and tested for it early on. eZ Publish legacy, on the other hand, was first created back in 2001 and has a long range of extensions built for it closely depending on how it was written. And as eZ Publish is considered mature software, backwards compatibility breaks are avoided as much as possible. This means that there are a few deprecation warnings to be expected when running eZ Publish (legacy) on PHP 7 which won't be fixed as they risk breaking extensions. This includes: