PHP5 introduced a whole lot of new functionality so chances are your PHP5 script has functions within it that PHP4 doesn't recognise. When choosing hosting insist on PHP5.
For the same reasons your car doesn't run on coal and Firefox doesn't run in MSDOS. Besides, there's a hell of a lot of compatibility with PHP 4 and 5.
Because PHP5 scripts are PHP5 scripts, and PHP4 scripts are PHP4 scripts. Now, want me to tell you about PHP6? lol
Are PHP 5 servers backwards compatible with PHP 4? Or will it just melt like when you try to use PHP 5 code on a PHP 4 server?
They're backwards compatible... although some commands are "deprecated" which means don't use them for new code because they will be dropped in future PHP versions.