Unfortunately not. Those PHP versions still have a lot of usage - PHP 5.5 and below accounts for over 65% of all PHP websites according to w3techs. We can't shut out that many people.
PHP 5.2 is now below 10% so it will be ditched in the next version. However, when development on v1.8 started it was higher so I decided on that as the supported version and cannot change mid way through.
The security issue is not as big a deal as it seems. Firstly, many server operating systems (like Ubuntu or CentOS) back-port fixes from later versions - so if your version says PHP 5.3 you will likely have security fixes from 5.4, 5.5 etc. Secondly, it's almost unheard of that a security issue in an old PHP version suddenly makes all sites on that version vulnerable. It usually depends on very specific and rare circumstances.
Speed is of course a great reason to upgrade but it's up to the users of Q2A to do that. We strongly encourage everyone to be on at least 5.6 if not 7.x.
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July 15, 2020: Q2A 1.8.5 released!