Changing the file extensions won't change the version of PHP that's installed on the server. If your host only has PHP4 then you can only use PHP4 unless they're willing to give you PHP5. The only way this will work is if your host already has PHP5 running and has it setup to only work with files that have the .php5 extension (this is an entirely possible scenario).
I'd say the first thing to do is to create a simple phpinfo file, like below, and name it with the .php5 extension and see what it says.
<?php
phpinfo();
?>
phpinfo() will give you the PHP version in big bold text at the top of the file. So if a file with .php says it's PHP 4.x and a .php5 file says its PHP 5.x, then your host has both installed on the server and is telling Apache to use PHP5 with .php5 files and PHP4 with .php files.
And on a side note if your host has register_globals turned on and they won't turn them off, I'd recommend putting the following in a .htaccess file at your document root.
php_flag register_globals off