Some hosters have the possibility to switch to PHP 5 with a directive in the .htaccess

AFAIK Publisher has been written /updated from module Smartsection with PHP 5 in mind.
It is possible to rewrite some statements to be PHP 4 compatible, but that would be a tedious task and a waste of time.
EG the (..)-> construct can be broken in two statements using an intermediate variable.

Let your client inform at his hoster for the possibilities of upgrading to PHP 5. If there are none, instruct him to look out for another hoster. Else he has to be content with a more simple and less fancy module and dito functions on his website.

Some hosts require you to add AddType x-mapp-php5 .php as first line in you .htaccess to turn on php5.

If you don't have .htaccess, make it, and add "AddType x-mapp-php5 .php" in it.

Check your hosters documentation, because the directives to use may vary. Eg.

If the wrong directives are used, you may have a 500 - server error as result.