Those are Drupal files, they are required by every page on a Drupal site.
cron.php is a Drupal generated/maintained file, editing it is not an option.
The paths are relative to the location of the cron.php file.
There is only one cron.php file so the same one is being executed.
The normal method is to set cron to open open the page via wget or lynx, but that is disabled at lunarpages.
For some reason "php ..." can open the included files and "/usr/local/php5/bin/php cannot ..."
The permissions for the included files are the same as for cron.php (755)
Currently I have the module that requires php 5 disabled.
cron.php works via the web browser under php4 and php5 and calling php via cron works as well.
I just can't figure out how to use php 5 via cron.

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I created a file that calls phpinfo() and executed it under php 5
Via browser ...
Configuration File (php.ini) Path /usr/local/etc/php5/cgi
Loaded Configuration File /usr/local/etc/php5/cgi/php.ini
include_path .:/usr/lib/php:/usr/local/lib/php
open_basedir '.:/proc/uptime:/tmp:/home:/usr/local/lib/php:/usr/home:/usr/local/bin/'
Via Cron ...
Configuration File (php.ini) Path => /usr/local/etc/php5/cgi
Loaded Configuration File => /usr/local/etc/php5/cgi/php.ini
include_path => .:/usr/lib/php:/usr/local/lib/php
open_basedir => '.:/proc/uptime:/tmp:/home:/usr/local/lib/php:/usr/home:/usr/local/bin/'
Those settings are the same, I am not sure what other settings would be relevant.
UPDATE:
When I use the "php" command, phpinfo() returns HTML and reports a Server API value of "CGI"
When I use "usr/local/php5/bin/php", phpinfo() returns plain text and reports a Servver API value of "Command Line"
I have no if CGI vs Command line is making a difference here or if so how to correct it.