Problem/Motivation
D7's INSTALL.txt still mentions PHP 5.2 and MySQL 5.0 along with several other post EOL versions.
The community has been gradually updating D7's testing configuration on drupal.org in #3092260: [policy, no patch] Review and update automated testing config for 7.x branch.
The documentation page at https://www.drupal.org/docs/7/system-requirements/php-requirements is fairly up-to-date.
Proposed resolution
We need to decide on what minimum requirements are actually supported, and update all docs (+ testing config) accordingly.
In practical terms there's no intention to start introducing more modern PHP features that would break support on older PHP versions - for example D7 core will retain the long array syntax.
We do sometimes encounter issues where it'd be useful to use features that were introduced a long time ago in e.g. PHP 5.3 or 5.6, and it'd be helpful to have an official policy on where any cut off is.
Do any sites still realistically require PHP 5.3 support? Do any distros still support PHP 5.x?
There's no guarantee that the testing infrastructure for such old versions will remain available; it's getting increasingly onerous to set up those environments.