After configuring with mysql and apxs (./configure --with-mysql=/usr/local --with-apxs=/usr/sbin/apxs), I ran make and eventually got this:

Making all in main
/bin/sh /Users/will/Documents/php-4.0.5/libtool --silent --mode=compile cc  -I. -I/Users/will/Documents/php-4.0.5/main -I/Users/will/Documents/php-4.0.5/main -I/Users/will/Documents/php-4.0.5 -I/usr/include/httpd -I/Users/will/Documents/php-4.0.5/Zend -I/usr/local/include/mysql -I/Users/will/Documents/php-4.0.5/ext/xml/expat/xmltok -I/Users/will/Documents/php-4.0.5/ext/xml/expat/xmlparse -I/Users/will/Documents/php-4.0.5/TSRM  -traditional-cpp -DDARWIN -DUSE_HSREGEX -DUSE_EXPAT -DSUPPORT_UTF8 -DXML_BYTE_ORDER=21 -g -O2  -c main.c
/bin/sh /Users/will/Documents/php-4.0.5/libtool --silent --mode=compile cc  -I. -I/Users/will/Documents/php-4.0.5/main -I/Users/will/Documents/php-4.0.5/main -I/Users/will/Documents/php-4.0.5 -I/usr/include/httpd -I/Users/will/Documents/php-4.0.5/Zend -I/usr/local/include/mysql -I/Users/will/Documents/php-4.0.5/ext/xml/expat/xmltok -I/Users/will/Documents/php-4.0.5/ext/xml/expat/xmlparse -I/Users/will/Documents/php-4.0.5/TSRM  -traditional-cpp -DDARWIN -DUSE_HSREGEX -DUSE_EXPAT -DSUPPORT_UTF8 -DXML_BYTE_ORDER=21 -g -O2  -c internal_functions.c
internal_functions.c:32: `#include' expects "FILENAME" or <FILENAME>
make[2]: *** [internal_functions.lo] Error 1
make[1]: *** [all-recursive] Error 1
make: *** [all-recursive] Error 1

After searching the web, I found that my problem seems identical to bug id #9716.  That bug was closed and supposedly fixed March 30th, a full month before PHP 4.0.5 was released, but the bug appears to persist.

I edited internal_functions.c, changed the erroneous "n" characters (I suspect they were supposed to be \n rather than n) to line breaks, did make again, and the problem went away.