You should upgrade PHP or ask your host to. PHP 5.3 is really old (EOL'ed quite a while ago), insecure and should generally not be used in production anymore.
Well, PHP himself may have EOL'd the 5.3, but some distros still do maintenance updates to PHP 5.3 (basically meaning, they patch the PHP 5.3 themselves for found security issues). Perhaps most noteworthy distro to do so is RHEL/CentOS 6.0 (maintenance EOL november 2020). RHEL/CentOS 7.0 has 5.4, so that should still run SMF (but how long, if support for older PHP's is not a consideration?). I'm sure there are other distros and operating systems that have PHP < 5.4 supported and maintenanced, but frankly I'm mostly familiar with CentOS.
And CentOS is really popular as it is free, really stable, and has a very long support. One of the reasons that it is stable, is that they provide support for their packages, and thus does not force to upgrade major PHP versions for example. This is a huge deal to admins who has to keep these servers running. For example every PHP version upgrade is a pain, since you need to ensure that every software running in these servers is compatible with a new major PHP version. And many times they aren't, and then you have to patch that software by hand if possible and maintain that patching it in the future.
So yes, as a sysadmin it is a sad day to see SMF pumping up the requirements, hope it is for a good cause. Basically this means that SMF will not be hosted on these servers that use distro that has PHP 5.3 or older, or sysadmin has to start compiling and patching the PHP himself (sure there are 3rd party repos with newer PHP versions, but their maintenance is often shaky, and how much do you want to trust 3rd party repos?).
So as a sysadmin you want to keep things flowing from the distro's own reporitories, as it is the easiest and most safe way to keep your server secure and in working condition. And often this means that you may not have the most fresh versions, but as I explained, it makes sense and there is nothing wrong to it.
Often times I've found that easiest solution for me is to patch the software that requires a new major version of PHP for example to still support the older version. Couple of time I've found myself very baffled that why developers have sacrified the PHP 5.3 support for usage of array shorthand syntax in couple of lines of code
I hope SMF will reconsider it's pumped up requirements for the project.
