I have to agree that one should be using PHP 7.2. It also gives a nice performance boost to Matomo.
The required PHP version for Matomo is shown in [1] (5.5.9 or greater)
Can you please send me a link to the FAQ page mentioning 5.3 (e.g. to lukas@matomo.org) so they can be updated?
My mistake, I was skimming the docs only but overlooked the specially linked requirements. I would go further though and remove outdated PHP versions from that page and only recommend maintained versions.
Additionally, the error described by OP looks like autoloading is broken.
"I have a Hostgator shared hosting with PHP 5.5."
PHP 5.5 is EOL since mid of 2017. Can't you switch to newer version such as 7.2?
Matomo itself does not even display the required version according to [1]. Their FAQ talks about 5.3 - which is horribly ancient too.
[1] https://matomo.org/docs/installation/